Does the power supply suppose to fire it up? Some power supply only charge & won't fire, for example, my shaver won't shave when power is plugged in, a safety feature. Did you ever fire it up with main power supply w/o battery in it? If you have two charger, you could rig one up & directly connect to battery contact on the ballast & see if it'll fire up.
If you want to try a new bulb, I think it's UXL-75XE, it appears on ebay from time to time for $50-$100 or so, try it out.