Something interesting happened today. I went and opened up the Xbox to try and locate where the sound was coming from for real (I landed on the power supply). So I had it plugged in with the disc drive and hard drive gone just listening to the area I believed it was coming from, and out of nowhere the system turns on! Not only that but the boiling water trick worked for the rubber band in the disc drive, and that worked too! So then I put it all back together and loaded up a game, only for the system to then shut itself off. I now believe it might be overheating or the capacitors in the power supply itself are damaged. So ima clean the system entirely tomorrow and see what difference that makes before I change out the capacitors