How to fix the weird problam with my xbox 360 and what is thee problam.?

I've had my xbox 360 slime for 6 months now and it just started doing this funny thing when you touch the power on it want cut on but it will make the noise like it is. then if you push on the try on it makes a little ding like it s going to open but want. you also have to wait half a day til it turns back on for real. I dont want to take it back becuase theres a game in their and wal mart probable want let me keep the harddrive. and it has months of reach maps and cod maps on it + 23 upgrades from the microsoft network that were a pain to download. also has tons of games downloaded on it.so is it fixable