I'd attempt to replace the power supply with one that you can verify works. Unfortunately iFixit doesn't supply the part, but I was able to find one for you on [link|https://www.amazon.com/Xbox-360-Adapter-Microsoft-Console-100-240V/dp/B089NQPTSN/ref=sr_1_1_sspa?keywords=xbox+360+e+power+supply&qid=1701880936&sr=8-1-spons&sp_csd=d2lkZ2V0TmFtZT1zcF9hdGY&psc=1|Amazon]. Replace that part first, and hopefully that should resolve the issue.