At this point I’d definitely say either something in your PSU borked, or (possibly and) not having a grounded outlet while doing hard restarts may have caused some damage to the Mobo. In either case, it’s not great but salvagable. Hopefully the new PSU fixes it, but there’s a distinct chance that a worn out PSU isn’t regulating power to your mobo properly and caused one circuit or another to fry out.
I’ve noticed that onboard video chips sometimes go without much notice. Further inspection is that the cheapo mobo didn’t have enough heatgrease or an adequate heatsink on the graphics chip, and since the graphics chip is always working it’ll likely be the second hottest component after the CPU which always has some adequate cooling device on it.
I’ve had several laptops “die” where the onboard graphics chip just desoldered from the mobo due to overheating. Couldn’t fix it because I don’t have steady hands, so my best solder jobs end up looking like this:
“Eh, it conducts. Good enough.”