Looking through this thread, I didn't see where you mentioned what version of P96 you're using. I ran an A2000 with an 060 and PII card for a few years with a couple of hiccups at first, just as you're experiencing. Weak power supply attributed to part of it (strange artifacting on the display), but the other issue, where it would refuse to save your settings was the version of P96 used. The one and only version of P96 that worked really well for me was the one that asks for a donation at early install:
http://aminet.net/package/driver/video/Picasso96...others have already mentioned your 060 libraries. Be sure you've got the latest of those as well. And be sure the latest 68040 library is in there too, even when using your 060 card. Somebody else will be able to explain better why this is, but unless I'm totally off the mark, you need both of those libs installed (even if you're only running an 060 card) in order for everything to be kosher.
And as Damion mentioned, going through and hard deleting old config files throughout Prefs/envarc is a good idea. As an extra precaution, instead of relying on a warm boot after deleting, I'd turn the computer off, wait several seconds and then turn back on. Fun "haunted" stuff we sometimes deal with! :lol: