Regarding the battery dropping its voltage this quickly, the batteries used in most of these boards are common a lot of personal electronic devices, so there are a lot of cheap batteries on the market. If you buy one of the cheap batteries, or even a name brand one that's been sitting around for years, you are gambling with how long it will last.
If you have to ask what is necessary to re-flash the BIOS, I'd recommend you send it out to have it done. It is a simple process, but I've seen too many people smoke components to recommend doing this yourself unless you have experience. To answer your question though, you need a PS, Video card, keyboard, monitor, floppy drive, and the software to flash the BIOS. What type of each of these components depends on the vintage of the board, but most of them require older components that aren't available at the local computer stores anymore.
If you are interested in sending your RT board to me to do this for you, send me a PM, and we can set something up. I've done it for a couple of others on here already.
Many of the newer WS boards did not have a battery, but since you didn't provide serial number/vintage of your machine, I can only guess that your WS board was repaired/replaced at some point and Siemens updated the part number in the process.