Hey guys,
I have the exact same issue with my TZ5. For me it seems to be a problem with the contacts for the mode dial. If I push the mode dial up while turning the camera on, it starts with a white screen, if I firmly push down the mode dial while turning on, it usually works. Without pushing on the dial, I get the problem intermittently. I haven't tried to fix it yet, but I may take it apart and see if there are any contacts that can be bent into place. Any tips on disassembly instructions?
Cheers,
Matt