Chosen Solution
After a possible overheat I took apart and cleaned it. I let it set overnight and the next day it booted up just fine and I used it for about 7 hours and then I shut off and won’t stay turned on. None of the lights indicate that it to hot.
Apart of the motherboard maybe fried - the xbox 360 E goes for so cheap it maybe better to replace it. Did you clean the fan? It is working?