Hi Everyone, I fixed him! Thought I'd post it here in case anyone else comes across the same problem.
I hooked up Pleo to a variable power supply directly by removing the battery and connecting the power supply to the metal springs inside the bay that holds the battery. The black wire (negative) to the bottom-left spring (when holding upside down with his head looking away from you) and the red wire (positive) to the top right spring. If you look closely they are marked "-" and "+" next to the springs. The power supply was set at 7V and 0,17A. That caused Pleo to boot up when I patted his back to wake him up, but he kept resetting right away (continuously waking up with the "huh" sound" but not moving). By inserting an SD card with the LifeOS to reset him to default I was able te reset the software and Pleo was born again. After letting him boot up for the first time I re-inserted the battery and he operated normally again.
After a while he started doing the balancing trick again, doing it over and over. He keeps doing that unless you activate another state like hanging him upside down or putting him to sleep. When you put Pleo back down he immediately starts doing the balance trick again. If anybody knows what might be causing this I'd be happy to know! Resetting the LifeOS (either an upgrade or downgrade) doesn't seem to help. The POP OS seems to work fine but isn't as much fun