The Amiga can operate without the battery; a new one won't help if the old one has damaged the motherboard. The Amiga Technical Resource (
http://amiga.serveftp.net) has some good guides on repairing battery damage. If you're not up for fixing it yourself, there's a place in France that does excellent work on repairing Amiga motherboards. I haven't used them personally, but several members here on A.Org have nothing but praise for them.
EDIT: There's also a chance that your problems aren't due to battery damage at all. Make sure all chips are securely socketed and the pins are making contact.
