|> But it doesn't seem like connecting speakers would wreck a power supply.|
Sure they can. Just do a search for “speaker overload” or “speaker impedance” and you’ll find lots of information about how adding too many speakers and/or speakers with the wrong impedance can overload the source and at best, blow a fuse, at worse, burn the electronics.
That said, the Z623 is a set of computer speakers, so it should be designed to work with a normal sound-card.
Since the audio-device was on-board sound, it might have used cheaper components than a dedicated card, so it is possible that the speakers overloaded it, caused it to draw too much power, and blew the PSU. You’re lucky the motherboard didn’t die.
A couple of things to look out for in the future to prevent it from happening again are to use a good PSU, and not use a bunch of splitters to attach more speakers to the audio-adapter (especially an on-board one).