In XP, driver files that have been installed should be in Windows\System32\Drivers and the .inf files for those in Windows\INF
The drivers that came with Windows or any service packs should be in Windows\Driver Cache\i386 so if you see sp3.cab in there it's the driver cache for SP3 so you will know that you have SP3 installed. If the latest in there is sp2.cab then only SP2 is installed.
But the problem is likely that there is no correct driver in there, so you get stuck at the dialog box to search for one from a local folder or WindowsUpdate. If there was, it would eventually install itself and fix the problem if you just left it alone for long enough.
In any case the mouse should work in Safe Mode beca
It's pretty simple, you just go into the BIOS and change the SATA controller setting to IDE mode or Compatibility Mode (rather than RAID or AHCI) and then you shouldn't need any drivers. If you want it to run in AHCI mode, then you'll need a floppy drive and the Intel AHCI F6 Floppy driver for XP32, on a floppy disk. No the XP installer doesn't let you browse to any folder.
Best to use a XP SP3 disc, or you may want to try the unofficial SP4 where someone has slipstreamed all of the updates after SP3 into the iso
use USB is controlled by the BIOS then rather than handed off to any driver.