I have performed plenty of searches in the past about this Xbox 360 problem. One so called fix that is still showing up quite often is the “towel fix”, where you wrap the Xbox in a towel. All this does is overheat the console to the point that it may start working again. You NEVER want to do this as other people may suggest. This will DESTROY the Xbox permanently.
NEVER use the “towel method” when trying to fix your Xbox 360. Get one of the amazingly cheap guides here instead.