Try attaching an external monitor. That's a good way to diagnose a failed display v. a failed graphics chipset. If you get an image on an external monitor, that says the chipset is working but either the internal display or its cabling have failed. If nothing show up on the external, that suggests you need a new logic board--not an economically viable repair for most users.
The internal backup battery is hard to get to, and the bigger problem is no new ones have been made in years. The only new battery assemblies work only in the 17-inch, 1.67gHz PBG4:
Newer Technology Replacement PRAM/clock battery for PowerBook G4 17" Aluminum 1.67GHz systems
Some PowerBooks with serial numbers starting with W8 have huge display issues. Might check the serial number (but don't post it here for security reasons).
Could the installation of a new hard drive have caused the screen to fail?
Yes, if some components were not properly reassembled after the HD installation. However, if the display worked at least once after the new HD was installed, the chances of the HD swap causing the problem fall to the "not so likely"category.