1) Does you motherboard have onboard video?
2) Are you using an add-on graphics card?
Because this sounds exactly like what happens when you're using a video card but haven't disabled the motherboard's built-in video adapter. When you change the CMOS battery, the BIOS will probably reset to factory defaults, so your motherboard will "forget" that the onboard video was turned off. If that's the case, plug the monitor back into the onboard plug, go into the BIOS and disable onboard, then turn off the machine and plug the monitor into the video card. It should work now.
If not, then you likely have a more complicated problem. In either case, it would help to know the specs of your motherboard and video card (if any).