Yep, seen it way too many times and it always plays out the same way! When a cheap unit pops a cap on the 5V rail, it doesn't just die quiet, it sends whatever voltage it wants straight into the board and the VRM eats it. The real kicker is the PSU often survives or looks fine, so people blame the board and buy another one, then the same thing happens again. First thing I'd do is tell your client to never power that machine back on with the old unit still in it, because a half dead PSU will fry the replacement board too. If you want to save him money down the road, get him into a unit with proper overvoltage and overcurrent protection from a brand that actually lists its specs, not the 500W bargain bin stuff. Cheap PSUs are the one part where going budget almost always costs double in the end, and this is exactly why.

Learned the hard way that heat and a slide hammer are not the magic trick everyone makes them out to be. I used to parrot that same advice until I spent two days fighting one cup that would not budge no matter how hot I got it. What finally saved me was rigging up a puller with a grade 8 bolt and some thick washers to thread into the cup itself, then popping it with the slide hammer on that. The threads bite way better than the jaw tool and it pulls straight instead of cocking sideways. Now I soak them in carb cleaner overnight first and that alone has cut my worst ones down to a couple hours. Your lathe puller is the real fix though, once you make your own tool for a job like that you never go back to the store bought stuff.