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 troubleshootinghttp://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