You don't need to working battery to get any Powerbook 100 series working. A good power adapter is enough, 2 Amps for the Black and White models, the 3 Amps version for the 165c and 180c.
You actually need to remove the old battery as they are often shorted and prevent your powerbook from turning on. These can even kill you power adapter too as the fuse in the battery charging circuit on the logic board is rated higher than the output of your power supply.
Nico