I have a push button start washer when I push the button the lights come on but the washer will not start.
A good candidate is the control assembly. GE does not release technical data on their machines, but look under the console and see if there is not a set of tech notes and troubleshooting info in there.
I do not know if the lid switch would stop initial operation on your machine so by pass it to rule it out. If you are getting power to the control assembly, as it seems you are, but cannot get the machine to operate, the control assembly is probably the problem.