The heater is lit up like it’s on. The thermostat is lighting but the heater is not coming on.

Sounds like the gas control valve thermostat is bad.
Following link has manuals and troubleshoot for each type of gas control.
http://waterheatertimer.org/troubleshoot-gas-water-heater-thermostat.html#thermostat troubleshoot gas water heater thermostat

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

Check for error codes and service manual on following link:
http://waterheatertimer.org/How-to-troubleshoot-gas-water-heater.html#intellivent

Replace gas control valve
http://waterheatertimer.org/How-to-replace-Honeywell-gas-control-valve.html

Gene:

Water Heater Timers Save Money

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

lightly tap on the area where the wires are connected. the valve will stick at times. try that.

Your problem lies in the gas valve, it looks as if the solenoid is stuck in the open position.

check your thermostat sensor or the sensor that is on the back

Based from your comment, please check the thermostat. It this is already busted, Have it replaced.
Hope this help.

The pilot light has to be lit before gas valve will operate. That's a safety feature so the valve won't open and fill the garage with gas and possibly cause an explosion or fire. If you have a standing pilot and can't get pilot to stay lit, it's usually the thermocouple and it will need to be replaced. Once the pilot is lit, the gas valve comes on and heats the combustion chamber up to approx. 100° to 125° a thermostat controlled fan switch will close and bring the blower on.

The thermocouple must be in the flame of the pilot and producing a signal to the gas valve. Also check thermostat

If you need further help, I’m available over the phone at https://www.6ya.com/expert/craig_3fa289bf857b1a3c

check millivolt output,if it is in normal range(400-600)check for continuity on pressure switch,flame rollout and high limits.

Change The Thermostat Cause If Your Getting Gas But The Water Heater Doesn't Detect The Heat It Will Close The Valve. When Lighting You Hold The Button Down For About 30 seconds so the thermostat will detect flame and stay lit. Check To Make Sure The Thermostat Is Where It Should Be. Heres A Picture Of What It Will Look Like.


You Can Replace Them If Need Be Will Be Available At Sears Or Home Depot. Also They May Sell Them At other Local Hard Ware Stores.

Happy Fixing And Thanks For Using Fixya.com
Sincerely,
Michael Scott