After de-winterizing and filling the water tank, the water pump runs continuously even with faucets shut off. Only a small amount of water comes out when faucets are turned on.

Open hot water handle farthest from the water heater. Turn water on that fills the water heater. It will take several minutes to fill the tank. Let it continue to run until all air is out of line. Turn all other hot faucets on to purge air from lines.

follow this chart troubleshooting and fix it. God bless you
est and replace a high-limit cutoff:

1. Disconnect power to the heater at the electrical panel and post a sign warning others not to turn it on.
2. Remove the upper access panel and push the reset button.
3. Replace the access panel and turn the power back on. If the water is hot, the reset was the problem. If not, you'll need to turn the power off again and reopen the access panel.
4. Use a multimeter to test the cutoff terminals for continuity. If faulty, replace with an exact replacement part.

Drain a tank:

1. Shut off power at the electrical panel and post a sign warning others not to turn it on.
2. Close the cold-water supply valve and open a hot-water faucet somewhere in the house (to speed draining).
3. Attach a garden hose to the drain valve and run it outside the house.
4. Open the drain valve and allow all water to drain out.
5. To refill the tank, close the drain valve tightly and open the cold-water supply valve. Also open a nearby hot-water faucet. When a steady stream of water flows from that faucet, the tank is full and the faucet can be closed.
6. Once the tank is full, turn the electrical power back on.

Test and replace a relief valve:

1. Lift the spring lever on the valve to fill a small cup. Check the cup for sediment.
2. If no water spurts out, or if water continues to drip after the valve is released, replace the valve.
3. Cut power at the electrical panel and post a sign warning others not to turn it on. Close the cold-water supply valve.
4. Drain a few gallons of water from the tank.
5. Unscrew and remove the discharge pipe if used.
6. Loosen the relief valve with a pipe wrench, then remove the valve by hand.
7. Apply pipe tape to the threads of the replacement valve and screw it into the tank by hand. Tighten it with a pipe wrench. Screw the discharge pipe (if any) into the valve outlet.
8. Refill the water heater and restore electrical power.

Replace a drain valve:

1. Shut off power at the electrical panel and post a sign warning others not to turn it on.
2. Close the cold-water supply valve and drain the water heater completely (see above).
3. Unscrew the drain valve with a pipe wrench.
4. Replace the drain valve with an identical unit wrapping the end with pipe tape.
5. Refill the tank and restore electricity.

follow this steps and fix it. God bless you
Drain a tank:

1. Shut off power at the electric panel and post a sign warning others not to turn it on.
2. Close the cold-water supply valve and open a hot-water faucet somewhere in the house (to speed draining).
3. Attach a garden hose to the drain valve and run it outside the house.
4. Open the drain valve and allow all water to drain out.
5. To refill the tank, close the drain valve tightly and open the cold-water supply valve. Also open a nearby hot-water faucet. When a steady stream of water flows from that faucet, the tank is full and the faucet can be closed.
6. Once the tank is full, turn the electrical power back on.

Test and replace a relief valve:

1. Lift the spring lever on the valve to fill a small cup. Check the cup for sediment.
2. If no water spurts out, or if water continues to drip after the valve is released, replace the valve.
3. Cut power at the electric panel and post a sign warning others not to turn it on. Close the cold-water supply valve.
4. Drain a few gallons of water from the tank.
5. Unscrew and remove the discharge pipe if used.
6. Loosen the relief valve with a pipe wrench, then remove the valve by hand.
7. Apply pipe tape to the threads of the replacement valve and screw it into the tank by hand. Tighten it with a pipe wrench. Screw the discharge pipe (if any) into the valve outlet.
8. Refill the water heater and restore electrical power.

1) Copy following link:
http://waterheatertimer.org/Crossover.html

2) Add comment with clear description of water heater, fuel type, and pump?
Is this a pump problem or water heater problem?
Is this a water well pump?
Are you getting good stream of cold water at tap?
Which water heater do you have?
Is the heater new?
Or older heater that stopped working.

If you need further help, I’m available over the phone at https://www.6ya.com/expert/gene_9f0ef4df2f9897e7

10-30-12
Cost calculations for recirculation system vary widely.
These systems cost more, and they cause higher operation cost of water heater.

1) When pump is OFF, then hot water is no longer leaving the tank.
Most recirculation systems have choice of timer for setting specific times of operation, or thermostatic operation that activates pump when sensor detects temperature less than 90 degrees
BUT...

2) Condition of plumbing is suspect here because you are not receiving fully 90 degree hot water from the recirculation system.?.

Bad single-handle faucet cartridge, or bad recirculation check valve, are causes of crossover. Clean recirculation check valve with white vinegar. Replace worn faucet cartridge.
Test for crossover.
http://waterheatertimer.org/Crossover.html

3) There are other suspects, such as water leak.
Drips, broken pipe, bad TP valve.
Turn off all taps and put ear against pipe to listen for running water.
http://waterheatertimer.org/How-to-troubleshoot-electric-problems-with-water-heater.html#listen

4) High costs: Lifting single-handle faucet in middle will immediately cause cold water to enter tank. Even if no hot arrives at tap, because the cartridge is drawing both hot and cold in equal amounts when handle is lifted in middle.
Today it is more efficient to install dual-handle faucets so tank is not receiving constant dose of cold water when single-handle faucet is not used correctly or tediously.
http://waterheatertimer.org/9-ways-to-save-with-water-heater.html

If you need further help, I’m available over the phone at https://www.6ya.com/expert/gene_9f0ef4df2f9897e7

Turn main water off to the water heater, it may be a valve on cold side coming in to shut off. Next turn power off to the heater and drain the tank the drain will be located near the bottom of the tank.
You will need a water hose to connect to the drain to run water outside. Open a faucet hot side to allow you to drain the tank.

Upon reinstall connect the tank up and fill tank and open up hot side on one faucet at a time to purge out air from system before turning power back on. Make sure you have water flowing from each faucet's hot side before turning power back on.

If the lower heating element burns out the upper element will heat the top part of the tank then shutoff. homw depot/lowes etc should carry elements. 1 turn off breaker, remove element access cover (the 2 panels on the front of the heater) test for electricity at the reset button ( uppermost device in upper panel) to make sure power is off. 2 turn off water (I usually turn off the cold water main to stop water cross feeding into hot supply line back into heater) 3 disconnect the 2 wires on the lower element, test with continuity tester. shhould be no continuity between terminals and tank, but around 10 ohms between the 2 terminals. Check the thermostat for continuity if tank is cold thermostat should be closed ie zero ohms across the 2 terminals.
If stat is bad replace stat; disconnect wires push it up out of the spring clip insert new stat reconnect. If element is bad: drain tank. connect garden hose to tank drain valve, open tank drain valve turn water main on to clear rust sediment and get water flowing. Next remove filter screen from a hot water faucet then turn on ( a hot faucet upstairs or higher than tank drain). Now turn water main off, air will now go in through hot faucet and tank will drain, takes about an hour. Use a water heater element wrench about$10 to remove element(s) make sure no bits of rubber gasket are left in element opening- dig em out with a screwdriver if needed. Insert new element with its gasket and tighten. reconnect wires DO NOT TURN ON ELECTRICITY! BE SURE TO FILL WATER HEATER WITH WATER ! Turn water main back on -air will come out of the hot faucet for several minutes. When water runs without any air sputtering, turn off faucet and replace the faucet filter screen. check element(s) for leaks. turn breaker back on.

chk for shut off valve to heater , open if closed. Open hot water faucet and listen for water pump. if pumping givre it time to fill heater tank and start runnuing out offaucet. Air will be purged as pump fills the lines and heater. Shoer and bath need hot faucets open also to purgr air.

Since the cold water works, the problem is not the pump. Look for a blockage or possibly a major leak in the hot water system. if you have a kitchen sink and bathroom sink, are both hot water outlets not working? Does the water heater have shut off valve , or is its drain still open from when you winterized it (and the water running out to the ground instead of to the faucet?

Begin by turning off the gas at the tank and at the valve near the tank. CAUTION: Do not proceed any further if you do not know how to relight the gas pilot!
2) Turn off the COLD water supply to the tank.
3) Attach a garden hose to the drain valve at the bottom of the tank. Run the hose to a convenient drain location. Be careful if you use a real cheapy garden hose... some of these become very soft when hot water runs through them, and may leak! If you don't have a drain in the basement floor or suitable sump hole, you have my sympathies... this drain-down can take a while with a bucket! Oh... and be careful if you use a soft plastic bucket. It can also soften from the heated water so don't overfill it or burn yourself!
4) Open up the hot water side of any faucet. Open up the drain valve on the tank and allow it to empty. Miller time. That is, unless you don't have a sump...
NOTE: If the drain valve clogs, turn on the cold water supply to the tank to use water pressure to "blast" through the clog.
5) When the tank is empty, shut off the drain valve and turn on the cold water. This will loosen up more sediment in the tank through the churning action of the cold water in the tank. Let the tank fill partially and drain it again. In fact, if you find that the sediment starts to clog the drain valve, turn on the cold water supply to the tank, which will help loosen the sediment and blast it out.
If you have extreme amounts of sediment, you may have to repeat this procedure a few more times. Look at the drain water... if it is running clear, you are done. Shut off the drain valve, open the cold water supply and allow the tank to fill. Once water comes out of the hot water faucet, the tank is full and your task is done! Now, you can turn the electricity or gas back on to heat the water.
How frequently to clean the sediment from your tank...
This depends on the source and purity of your water supply. Some pros recommend doing it annually, some every few years. I would recommend doing a partial drain down annually if you find any sediment in the tank, otherwise every couple of years.
Remember that with an electric water heater, you must turn the power off! Even a partial drain down may expose the upper heating element to the air and permanently damage it!