There's finally an unofficial patch which fixes the problem(s) that prevented Sonic CD PC from running on Windows XP.
The patch works with the retail version of Sonic CD as well as with the Sonic CD demo, which can be downloaded from sega.com's support page. It does NOT work with the OEM version of Sonic CD, the oldest one.
The patch is intended for Windows XP, but it might work with Windows 2000 and Win 9x, too.
As always with free software: use it at your own risk, no warranties or anything.