Thanks to Edward Whelden, who emailed me this one:
Restart the computer in Safe mode. Use Windows Explorer to remove the file called 'ShellIconCache' from the Windows directory. (You must be able to view all files, including hidden files: click options on the view menu in Windows Explorer, click Show All Files, then click OK.) After deleting the ShellIconCache file, restart Windows 95/98 normally. Windows 95/98 will rebuild the file on startup