Err... I just checked the game in Xp - there are no troubles at all.
Don't run system tests in install, as for the all Sierra win9x titles in Xp.
Set the screen to 640x480x256 before the play. (with the display properties/settings/advanced/adapter/list all modes). Or edit the resource.win file - wwidth and wheight parameters (no movie scaling at all, by the way).

P.S. Sadly, but - you can install the game with DosBox/WfW311 combo, but the game is crashing at the movies.

I checked my XP computer and Shivers works fine. I think I have some Windows 3.1 floppies lying around, but I'm not sure. Have to check, but I at least can use it on that older computer for now.