First, connecting the battery is always a good idea.
Second, the serial cable is for monitoring and using it for power management. You'll need the software that goes with it. If it's a newer UPS, it will have a serial to USB bridge cable.
If it's an old one, if it's anything but a Powerware or an APC SmartUPS, throw it out because it could be anything, including dead batteries or a faulty circuit. Even the newer ones aren't worth fixing anymore. The batteries have to be gel cells and they're about $50 a piece. Considering the new APCs, the 650W ones, are about $80, you can easily see how it's not worth bothering with. The Powerwares, on the other hand, are the best units you can buy pretty much and they're worth a small fortune. The SmartUPS from APC are decent too and they're about $500 a piece. Then it's worth putting a few dollars into them.
