I have a GG40T06/487-246 GE SmartWater Water Heater, it is about 10 years old and now there is leak on the position of the stem of the reset button connecting to the gas valve. Any suggestions to replace gas valve or need to replace the whole water heater?

1) Copy following links:
http://waterheatertimer.org/How-to-troubleshoot-gas-water-heater.html#intellivent
http://waterheatertimer.org/Crossover.html
http://waterheatertimer.org/How-to-adjust-temperature-on-water-heater.html

2) Low temperature setting, extremely cold incoming water, Water leak or broken pipe running hot out of tank, crossover caused by bad faucet cartridge or bad recircirculation check valve,, bad gas control valve thermostat.

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

Make sure any water valves (Cold or Hot) for water heater are not leaking first. Gate valves may leak at the packing nut over time and drip on top of tank. If water is leaking from the top of the water heater itself the tank is corroded and water heater will need to be replaced.
RJ

12 year old water heater is getting near the end.
Some tanks last 20 years, but that's the exception.
To find exact age of your brand water heater:
http://waterheatertimer.org/pdf/WaterHeaterSerialNumberDecoder.pdf

Leaking TP valve:
1) Lift TP lever and gently lower back into position to see if that stops leak.
Occasionally something gets stuck in the valve.
2) Sometimes water heater temperature gets turned up because heater is not producing as much hot water as before, and higher temps cause TP to release pressure because of overheating.
Dial temperature down to 120 degrees.
http://waterheatertimer.org/How-to-adjust-water-heater-temperature.html

3) If steps above don't fix problem, replace TP valve >> TP valves have 125 or 150 degrees rating >>> older tank shouldn't be running above 125 because higher temps cause more pressure on tank, so thermostat should be lower than 125 degrees TP rating.
Buy replacement TP at any hardware store + a roll of teflon tape to seal pipe threads.
Turn gas control to pilot ... this will keep pilot lit but burner will not fire.
Let water cool, and then drain some water out of tank.
If TP valve is on side of tank, then open drain on side of tank and drain water until it is lower than valve level. Open bathtub spigot to let air into line.
http://waterheatertimer.org/Water-heater-will-not-drain.html
Be careful around water that is higher than 120 degrees F >> you can get burned quickly >> apply cold water to any burn.
Use pipe wrench and unscrew TP valve counterclock-wise.
Install new TP and put teflon tape on threads.
Re-fill tank completely and open tub valve on hot side until water is running >> then turn gas control back to original position.
Do not fire up any water heater before tank is completely full of water or this could damage tank.

To read more preventative information about water heater leaks and age problems:
http://waterheatertimer.org/Water-at-bottom-of-water-heater.html

Bad reset mechanism.

It sounds like there is air in the line, so open the gas line just a little for a few short seconds to let some gas out, after that, keep the one red dial on pilot then turn the other to about medium. Light the pilot by depressing the red button, then once the pilot is lite, continue to hold the red button for about 1 minute, Once that is done slowly release the button and then turn the dial that is set to pilot to on position and give it about 1 hour to heat up

Hi try to tighten the cover first if heaters good look at price of regulator change

Look and see if your pilots flame is touching the themocoupling ,if it isnt then cleane your pilot orfice.If that dosnt work replace thethermocoupler.I would also check the draw. Hold alit match or a cigerett up to the draft diverter (the air space between your heater and the vent. If it dosent draw the smoke up the vent it meanes your vent is stoped up or you need to raise it.

Something you can do, following your fathers logic,   is to attach a hose to the drain of the tank and run water from the bottom of the tank into a drain untill all the sediment is removed (Water runs clean). This is normally done once a year as preventive maintenance  on all tank type water heaters. The logic sounds good to me. 

Try this, turn the black gas ****, on top of the control box, to the Pilot position. Set the temp. control on the front of the box to the desired temp. Then, hold a match or whatever else you use to light it, next to the end of the pilot, then, while holding the match to the pilot, press the reset button on top. When the pilot lights, continue to hold the reset button down for about 1 minute. Then, after a minute, turn the gas **** to the ON position, then it should remain on.

most units from GE come with a 3 year manufactures warantee and the home depot should have no probleme giving you a new one off the shelf with your receipt they will send it back and get there money back from GE so they pass it on to you. it would cost you the same amount to fix that one then to buy a new but yours is still under warantee untill july. hope it works out for you.