I was in the same position, so I mounted the drive under a different LiveCD, deleted the frugal install, then ran Puppy again and did a full install. That worked for me.

The combination of 25.16 and Xvesa did the trick. Thanks everyone for your help, it's much appreciated. Xvesa also seems to use 60MB less memory than Xorg, which is a big saving when you've only got 128MB to begin with.

Yeah, I think the HDD is some weird SCSI-IDE hybrid like yours, so that makes sense. Where can I get a version with the older kernel? Would 4.3.0 do the trick?

I've got a LiveCD of Puppy 4.3.1 that works well with my ancient Thinkpad laptop, except that it can't find the hard drive. I don't have a floppy drive and that seems to cause some problems. I'm pretty sure that the drive is physically in working order, since I can see it under other LiveCD distros....