The 3000 was unique among Amigas in that the battery actually backed some vital memory location with system (video settings?) info in it. IIRC, there was a utility on Aminet that reset those values to defaults in case they were lost. Maybe the battery needs some up time to recharge (as has been pointed out. I think the battery is a rechargeable NiCad.).
I wonder if the VGA-out is working now. Have you tried it since getting the 23-pin video connector to work? It might help to set the trim pot to mid-range and tweak from there for best VGA image quality.