Lovely. I'm afraid that you will probably need to do a follow up job to clean up the mouse urine. The creature is likely to have fouled in some unusual places, so with the case open, shine a torch around and look for staining on the chassis. Fouling of the chassis is a minor problem (the steel may rust prematurely, but only on the surface), but any "splash back" may have gone on to adjacent switches or PCBs which could be damaged in the long run.
Have you thought about providing a snug, disposable mouse nest in your workshop or storage area so that if you do get unwelcome visitors, they'll be attracted to that rather than your Macs/car upholstery/random boxes of vulnerable junk?
I think that your analysis of the state of your G3 PRAM battery is about right. From the beige G3 onwards, many Macs with flat batteries boot fine; the network settings are often sufficient for the Mac to connect to the internet and to reset the internal date/time via NTP. TCP/IP and internal time are all that they need for most purposes. I ran an iMac G3 500MHz with flat PRAM battery for a couple of years without problems. I wouldn't expect a PCI PowerMac to be so forgiving.
It is improbable that incorrect DIMMs are the source of your boot problem. Different DIMM formats have a different key format, so without a lot of violence, it is impossible to insert DIMMs that will cause permanent damage. It may be possible to fit parity DIMMs in a way that upsets the PowerMac's CUDA/PMU. Installing a full power battery is the only way to start analysing the problem further -- and no Mac enthusiast can have too many PRAM batteries.