Sounds like you found the guilty party. Best if you check thermostats or fuses for continuity with power off and one wire removed. Next thing you can do is to install temporary jumper and fire up the appliance to check if that is the only problem. This is non resettable thermostat, replace it.
The flame sensor Part number: WB27X10461
Here are the breakdown diagrams and Interior parts for GE JES1651SJ02 - AppliancePartsPros.com
Post the results.