Do you mean power windows or power mirrors or both?
With a bigish list of system failures I would start to wonder if either an AM fusible link had failed (square looking plastic cubes with clear lids in the under bonnet fuse box) or if there was physical damage in the under bonnet fuse box. I think there's an AM fuse that covers a few of the systems switched by the accessory position on the ignition switch but I don't have the EWD book to check at the moment
Taking the previous owner's story at face value I wonder if a clumsily plonked battery might catch the loom/fusebox and do something unpleasant.
Memory eludes me on the exact details but if you unbolt the fusebox from the inner wing it can then be further disassembled to give access to the wiring harness connectors - there may be a couple of bolts in the fusebox which hold it together
Issues with these connections are not unheard of so have a good poke about and check for corrosion
Regarding the brrrrm, tish dump valve thing - if what you reconnected was the big flying saucer thing circled in red then that is the OEM dump valve