Reliance gas 602 water heater .. The burner is lit and going but I have no hot water coming out???

time to replace. The flame arrestor is most likely dirty.

Reliance
2nd and 3rd digit of serial number is year
C05 is 2005

What color is flame? Should be clear blue.
Pilot is burning so thermocouple is good, and sitting in pilot flame.
Pilot flame should be clear blue.
Otherwise clean burner parts.

Is water at tank hot??
If burner is not turning on, the gas control thermostat is probably bad.
http://waterheatertimer.org/pdf/How-to-replace-water-heater-gas-valve.pdf

Otherwise more information is needed.
http://waterheatertimer.org/How-to-troubleshoot-gas-water-heater.html

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

Reliance water heater?
Thermocouple is good if the pilot stays lit continuously.

501 is older model. Unknown if this unit has FVIR protection and sealed combustion chamber or open air intake on front of unit.
http://waterheatertimer.org/pdf/Reliance-2006-Service-Handbook.pdf

With FVIR protection:
Get more fresh air to the unit.
Clean the flame arrestor screen.
Test and replace the thermocouple:
http://waterheatertimer.org/How-to-test-water-heater-thermocouple.html
Inspect and clean burner and combustion parts
Test gas pressure, bleed air out of gas line.
Replace gas control valve.
Test draft air by lighting match and see if smoke is pulled into the vent pipe at draft hood on top of tank.

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

If I understand correctly, the pilot light is not staying lit.
You light the pilot and water in the tank reaches temperature.
Once hot water is gone, then pilot light has to be lit again.

Gas pressure is good, and gas is flowing.
Thermostat is working at high end because it cuts off heating.
Vent is working because tank heats up.
Air intake is working.

Gas control thermostat might not be reading low temperature. Replace gas control valve.
Pilot tube might be dirty. Clean burner parts and combustion chamber, and air intake, and vent.
Backdraft might be blowing out pilot. Check for constant updraft by running water heater 5 minutes, and then light match under vent hood and see if smoke goes up.
Very hot air can put out pilot, especially when water heater located in attic. Add ventilation.
Improper vent might have water dripping back down into combustion chamber and putting out pilot light and rusting out the parts. Inspect for rusted parts and water.
http://waterheatertimer.org/How-to-install-gas-water-heater.html#troubleshoot
http://waterheatertimer.org/pdf/Pilot-light-will-not-stay-lit.pdf

Can be gas control valve. Or possibly the burner parts and air intake need yearly cleaning.
Open following links for example illustrations and useful troubleshoot resources:
http://waterheatertimer.org/How-to-install-gas-water-heater.html#troubleshoot
http://waterheatertimer.org/pdf/Flame-Arrestor-Screen-Cleaning.pdf
http://waterheatertimer.org/pdf/How-to-clean-combustion-chamber.pdf

Your manual will have additional information:
http://www.reliancewaterheaters.com/lit/om/g606.html
http://www.reliancewaterheaters.com/lit/om/manuals/186486-002.pdf

Hello Mike,
Check gas pressure, burner parts need to be cleaned, check electrical outlet, hot surface igniter is bad

White Rodgers intellivent error code:
http://waterheatertimer.org/How-to-adjust-water-heater-temperature.html#Intellivent
http://waterheatertimer.org/pdf/Intelli-vent-gas-valve2.pdf

Error code says: system in lockout, but you know that.
1) Low gas pressure, no gas to water heater: call gas company to check pressure
2) Hot surface igniter not positioned correctly: inspect and clean burner parts.
http://waterheatertimer.org/images/Reliance-hot-surface-ignite.jpg
3) Low voltage to water heater/ outlet has wrong polarity: Use circuit analyzer on electrical outlet to make sure polarity is correct

Typical power vent manual:
http://waterheatertimer.org/pdf/Reliance-40-50-power-vent.pdf
Cleaning water heater:
http://waterheatertimer.org/How-to-install-gas-water-heater.html#clean
http://waterheatertimer.org/pdf/How-to-clean-combustion-chamber.pdf

Its an ELECTRIC hot water heater yes?
No burner or pilot then hey!!

OK, make sure your ON-Pilot-OFF knob is turned to "ON" after you light the pilot. Then make sure the temperature dial is not set at vacation setting. It should be set to atleast mid range between low and high at the "A" or triangle symbol, depending on what dial you have. It will take 20-30 minutes for the water to get hot, but the burner should come on right away after it has been relit. If not, you may have to call your local gas co to look at it. Douglas

The paid answerers might have a specialist in your model of water heater.
As a free answerer, I specialize in providing resources that might help you for free.
When you say the gas control pieces, I assume you mean you replaced your entire gas valve with a generic dial-type gas valve.
You replaced thermocouple, but you did not replace burner assembly that includes the pilot tube.
Your other gas appliances are working fine.
You have not installed a new gas furnace with a blower that is vented up the same chimney as the water heater.
You have put your hand near the vent hood to see if there is backflow coming into the water heater when the furnace turns on.
You have removed the vent hood to give you access to the vent pipe, and you lit a match and the smoke from that match drafted upwards. You have done the lighted-match test when the furnace turns on which reveals the general condition of the venting stack.
You have checked your outdoor vent stack to make sure there is no obstruction, or the vent hood is not missing.
The burner flame on the water heater is a clear blue color with very little yellow. This shows the quality of the combustion air and reveals if amount of gas flowing to burner is restricted.

http://www.thetankatwaterheaterrescue.com/forums/forum3/

http://www.reliancewaterheaters.com/prod/gas.html
Reliance is an AO Smith company
The site doesn't have a manual for the 501
I e-mailed Reliance several weeks ago asking for a 501 manual.
They send a generic gas water heater manual with no troubleshooting

http://www.reliancewaterheaters.com/lit/om/g616.html
Link above shows a typical Reliant heater, the 616
Age of your water heater can be seen on serial number.
The two numbers following first letter are the year water heater was made.

http://www.reliancewaterheaters.com/lit/om/manuals/186486-002.pdf
Troubleshooting begins on pg 29
Troubleshoot flowchart begins on page 31
The new gas water heaters have the FVIR system so troubleshooting includes that information.
I don't think the 501 would have a FVIR flammable vapor prevention because it is older
The new systems have an igniter
The troubleshoot flowchart gives valuable information

The Reliance 606 has an enclosed thermal couple. Before you try taking that assembly apart take a wire brush to the bottom opening directly under the burner. There is a metal filter on the very bottom of the water heater. It could be that the filter has gotten filled with dust or animal hair. It took a serviceman 2 days to figure this out for me. The water heater has to have good airflow through that filter to work well.