I'll put in my two cents here having done trouble shooting on a couple hundred 4000's.
1. Unplug the accelerator card, blow out both it's slot and the accelerator slot on the motherboard. If you have any contact cleaner, use that as well. You may have gotten a peice of fuzz or dirt in there when you took it all apart to replace your battery. Put it back together and see if she boots.
2. Unplug the riser card, does the machine boot without it? If it does, check the riser card for a shorted resister leg, quite often they were too long, and in the process of pulling it out you may have touched one to another, or when reinstalling it you've managed to short the case support crossbeam to one of the legs.. While you have it out, clean it's slot as well, can't be too thurough.
3. Remove the motherboard again, and, with a magnifying glass and good lighting, visually inspect the area you worked on. Maybe you got too much heat near another component and have inadvertantly desoldered it, or turned it into a cold solder joint. Or maybe you dribbled/splashed some solder on a nearby component.
Lastly, you may have managed to cause a component on the motherboard to come loose just by torque. Quite often poor soldering on the motherboard will go un-noticed for years until you physically remove the board and bend it ever so slightly and in the process cause a poor solder joint to crack or come loose. This is a bitch to track down by eye alone, but with patience and a sure hand you can go retouch most of the "obvious" solder joints with a 60watt iron and redo the welds.
If worse comes to worse Amiga France (Amiga.fr) can fix your board (they have the equipment to test and repair any Amiga motherboard faults). I've used them for a few boards and have yet to be disapointed. They aren't cheap though, usually it's 100E per board by the time you get it there and back.
I hope it's just #1 for you. :-o
