I have described - if not explained - all the occurrences you mentioned.
Now it is back to: you have grounded the PC PSU chassis; you may have grounded the inverter chassis; you may have broken a ground loop (the broken AC earth/green wire between inverter and PC-PSU).
Without an AC earth (inverter to PSU) is that if the PSU has an internal AC to chassis (earth) fault, its fuse will not operate.
But you if your inverter output earth (green) is somehow dc connected to ground, then both earths are ground and that fusing or protection should operate.
I'll leave it to others to translate the above and all earlier for you - they put it better and simpler.
(If others need to PM me for clarification... Though in this case I'll probably break my "only respond to OP" rule. [ Which I regret breaking when long WASTED hijacks occur (like voltage isolators versus UIBI in a CAR with a CHARGE LAMP!) but have no(?) regrets breaking (Read: Ignoring) when it corrects or informs or qualifies gurus replies....] Maybe I could find some connection diagram?)