Just did the work-around provided by gian-ava and my site is running fine now. Avatars upload properly, can be cropped and saved like the system should. It’s funny though because I have the same versions running on another domain and have no problems at all changing avatars, saving or cropping.
Got it working with all the great help. Thanks! I’m looking forward to when BuddyPress comes out of beta and the photo galleries are connected now that the forums seem to be working quite well.