When the hot water heater is running water leaks from the chimney. the pipe from the heater to the chimney is dry upon removal. about 3 gals. of water leaks from the chimney with two showers.

Check if your shutoff valves are leaking. In a cold climate is the exhaust line partially blocked, and causing condensation to form on the pipes. Condensation forms and runs off of the cold water line to the tank. Try insulating the cold line. You can get preformed pipe insulation sleeves for about 1.00 each for a 3 foot piece.

test the thermostat and the heating elements --also there are resets that can pop push and make sure they have reset

Very simple - call a Plumber. He will fix your plumbing problem, and any foreseen potential problems related to your water leak. He may also suggest replacing your 6 year old water heater. Of course ..... for a professional cost.
However, depending on your time, skills, proper tools, patience and luck, it's easy enough to perform yourself:
1. Switch off the water heater Breakers (220v) in your service panel.
2. Turn off the water supply to the water heater.
3. Attach a water hose to the drain faucet. ( a good time to flush sediment -calcium deposits)
4. Open a hot water faucet to vent (above the level of the water heater drain - kitchen sink)
5. Remove the suspected leak components. (a union connection is a good place to start)
6. Install New pipes -3 wrap all male threaded ends with teflon Tap. Tighten securely - using 2 wrenches.
NOTE: Before refilling - you can turn on the water heater supply valve for a few minutes, to flush out any lingering calcium debris.
7. Shut off drain valve - remove hose. Shut off venting hot water faucet.
8. Turn on water supply valve to fill water heater.
9. Open a hot water faucet to relieve air pressure while filling - preferably the bath tub faucet, it doesn't have a screen that might clog.
10. When water flows without air - shut off tub faucet.
11. Look for leaks.
12. Switch the water heater Breakers on.
Note: 50 gallons should take an hour or more to heat up. Turn on a hot water valve momentarily within this heat up time to relieve thermal expansion. ( the PT valve on your water heater will perform this task if pressures/temperature exceed new water heater tolerances - it's just a precaution to introduce these fluctuating pressures on your fragile 6 year old unit)

These are just basic instructions - assuming you fill in the common sense and work safe steps.
Good Luck - The Skill will only come after trying.

Also open cover and check if element is leaking. Elements frequently leak at rubber seal.
Next suspect is rusted-out tank that is leaking through a thin-place in the tank.

Otherwise there are not many other places to check if pipes are dry, especially with the Atwood 10 gallon.
I suggest replacement.
http://waterheatertimer.org/Water-heater-is-leaking.html

Add a comment for more free help.
Also take advantage of fixya expert assistance live.
For a price, expert works with you while you work on water heater or any do-it-yourself project.
Fixya is always less expensive than a service call.

Id try raising the chimney until you can get the smoke from a piece of paper to get sucked up under the draft hood. I believe theres a different problem then a cold pipe.raising the chim.might not be the answer.

A leaking water heater cannot be repaired, assuming it's the tank leaking and not nearby water pipe.
http://waterheatertimer.org/Water-heater-leaking.html

First thing is to protect your property from catastrophic tank failure where tank ruptures and water runs until it is shut off:
Tanks are under pressure when they are hot.
Close cold water shut-off located above tank.
Turn control knob to 'pilot' so pilot is lit but burner will not turn on.
Open hot side on tub for few moments to relieve tank pressure.

Now your property is safe.
You need a new water heater.
In mean time, gas water heater makes 41 gallons hot water per hour.
Shower used 5-9 gallons hot water.
Bath uses 10-15 gallons hot water.
You can turn on water heater for short stretches and limp by until you get a new heater.

Steps for installing gas water heater:
http://waterheatertimer.org/How-to-install-gas-water-heater.html

Gas or electric?

1) Electric heater can be completely covered with insulation except TP valve. Set electric heater on insulated surface. Insulate pipes completely right down to tank.

2) Gas heater is different.
No insulation over combustion area, or gas valve, or air inlet or. No insulation on top of tank that will interfere with venting of dangerous combustion products including odorless CO gas. Foam insulation on pipes should stop 10" short of tank top. No insulation within 6" of the 3-4" inch galvanized vent pipe.

Here's photo with gas water heater insulation tips:
http://waterheatertimer.org/images/Insulate-gas-water-heater.jpg
http://waterheatertimer.org/9-ways-to-save-with-water-heater.html

3) Tankless gas. No insulation on box. No pipe insulation within 12". No insulation near vent pipe.

4) How much clearance between heater and chimney?? Not sure what that means. Is that the water heater vent stack? Or where vent stack goes into chimney stack? No insulation on gas flue pipes. Or within 6 inches of 3-4" water heater vent pipes

5) Is insulation fireproof? Everything burns if it's hot enough. If you throw insulation into backyard fire, paper and foil will burn away and insulation kind of falls apart in the heat. Fiberglass insulation cannot be set on fire with a match. Foam pipe insulation will burn.

That is normal, the heat just rises from the hot water, the pipe on the right should be cold and if you were to run hot water anywhere in the house it will immediately cool of the cold inlet pipe and you can feel it

3 minutes?? does the water run cold then? or just warm?
Is this what the tank you replaced was doing? If so, then you may have: 1 a recirculating pump instant hot water system thats faulty and allowing cold water backflow into hot water piping. 2 A tempering valve that has stuck, allowing cold water into your hot water system.
Or maybe a broken or missing dip tube in your new heater.
If after 3 minutes the water is coming cold out leave that faucet running and go to heater and feel the hot water outlet pipe from the heater. if that pipe is hot then the heater is not the problem. If the hot pipe from the heater is cold the heater is the problem. (Make sure the cold pipe coming into the heater is connected to the Right side marked "cold" !) If there is a tempering valve by the heater: feel the output from the tempering valve, if it is cold and the pipe from the heater to the tempering valve is hot, then the tempering valve is the problem. If all these are OK somewhere in your plumbing system hot and cold may be connected possibly a faucet or showerhead that is shut off at the spout/head, but hot/cold handles are left turned on then cold water can backflow thru hot pipe.

A draft inducer blower is used to create a proper draft in a chimney or exaust pipe from your water heater or furnace. In a high efficiency furnace or water heater, there is not enough heat expelled from the unit to the chimney to create a proper draft. The toxic carbon monoxide gas which is expelled through the chimney from your appliance is normally carried upward due to the rising hot air in the chimney. When appliances got more efficient (putting more heat into the water tank and less going out the chimney), manufacturers had to add this blower to help get the gases out the chimney since there wasn't enough hot air to create a draft.
Hope this helps.