sounds to me like its an old xbox.. not a 360, at least i hope not lol... umm hmmm... list of things id try...
1. make sure its all the way plugged in.. ive tripped over cords and half unplugged them without knowing lol..
2. check the contacts on the power cord and see if they look burned....
3. at this point id prolly yell at it and smack it a few times and give up for a day... (yes ive broken a radio and my psp.. i threw the radio out the window and it worked after that... psp wouldnt charge so i dropped it few times.. now it works LOL and im serious but i don't recommend doing it if you don't mind buying another one anyways)
4. lol next day id open it up and see if it has a fuse, which could have burned out.... easily replacable if that's the case (don't quote me on that.. cause i don't really know but most fuses just pop out and back in)
5. if nothing else find someone who knows alot about modding and ask them what it may be...
ive never had an xbox but those things are just general electronics trouble shooting... so should aply to most everything cept the fuse.... not everything has one but high power stuff like my surround sound has one and ive burned it out before ampping the hell out the signal (oppss lol)