A flat backup battery would almost certainly not cause this behaviour (it's not called a PRAM battery). In fact, though you do need a backup battery for "real" use, the machine will likely function well enough for tinkering purposes without one. However, there might just be life in the original cells, but they take days and days to charge and that can only happen if there is a viable main battery already charging. Occasionally serendipity strikes with these things.
The real trouble is the main battery, but because these are NiMh cells, there are some things you can try.
1. Stick them in the freezer for a day or so, remove, let them thaw and dry, and then recharge (google NiMh, freezer trick and dendrites).
2. Get a copy of Apple Battery Recondition (in fact, with a stock System install, it ought already to be in the Apple Extras or Portables folder) and cycle the cells a good 8-10 times, with some overnight periods plugged in. You can sometimes bring "dead" cells up to a 45 minute or so charge through steps 1 and 2 alone.
3. Battery Amnesia is a Shareware utility that could be used instead of #2.
4. Repack the battery with fresh tabbed cells of identical size. Would not cost much to do. $25?
5. Repack the battery with a couple of Radio Shack AAA battery holders and off-the-shelf normal AAA NiMh cells, copying the number of cells, the wiring and the arrangement of the fuses/ sensors in the original battery pack. AAA cells would fit inside the case and will have roughly the capacity of the original cells (at somewhere around 900-1000µA), so the software controlling them (in the Power management system that you are resetting) will know what to do with them. Higher capacity cells are a bit hit and miss in these old machines, so I would not pay any price premium for them.