I've been barking up the wrong tree.
The offending game was Doom95. (I know, there are thousands of DOOM ports that work under every OS, but the point was to test this
one.) The mouse didn't work under Windows 98 SE, and the documentation had lots of vague unhelpfulness about mouse compatibility issues in it, so I figured I needed Windows 95.
No, dag gum it, what I needed was the .VXD file that Activision just forgot to put on the DOOM Collector's Edition CD. See: http://www.classicdoom.com/dmouse.htm
. Install that, and Doom95 runs fine under W98SE.
Thank you all for the help, anyways, but it looks like Windows 95 is going back in the can.