Chosen Solution
I have an OG Xbox that was in storage until now. I plugged it into the wall and the video connected to my Tv, but no lights or sound when pressing either the on or eject button. When opening the Xbox, I found three capacitors bulging and a burn mark on the top side of the power supply board. I have ordered all replacement capacitors for the motherboard, but what else can I do about the power supply? There is no output voltage on the power supply, no caps bulging either, just a burn mark on the topside. Will a PC power supply with enough amps connected properly work in powering it?
since we do not yet know why your PSU has gone off in smoke let me answer the later part of your question. Yes, you can use an ATX PSU to power your Xbox. Check on places like this to see what it is all about. Now on here you can see how you would need to connect the individual points from ATX to Xbox
Panasonic 6.3V 820uF 12mm Capacitor … (B95) replacements and Panasonci 16v 1500uF 20mm Capacitor…… (B3) to be safe and u should be good