Sounds like your power brick is having issues. Did you stop using your Xbox 360 for a long time? I had something like this happen to me after buying an Xbox One. So, after about 6 months of not using the 360, I wanted to play something, and the console won't power on. I brought it to a shop to diagnose, and the issue wasn't the console, but the power brick. I ended up buying a 3rd party one (fat Xbox 360).