I found the solution. Here is the text from the Eidos support page:

This problem is specific to the Platinum Series version of the game. The Platinum Series version of Final Fantasy VII has the disks labeled: Disk 1, Disk 2, Disk 3 and Disk 4.

Disk 1 is the Installation disk and cannot be used to start the game; you need to use Disc 2 instead. After the installation of the game is complete and you are prompted to insert Disc 1, you must insert disk number 2 into your CD-drive. From here click OK; or re-launch the game from the Start menu of Windows by going to the Final Fantasy VII listing under Start>Programs>Final Fantasy VII.