bryan29, do you still have the old computer? From your original post you said the CD-Rs that are unreadable on your new computer (Windows 7) are still readable on another computer. Is that other computer the old Windows XP computer?
Did you burn these CD-Rs on the old computer? If you're willing to physically open up both computers, you can temporarily remove the CD/DVD drive from the old computer and connect it to the new computer to see if the unreadable CD-Rs work in the old optical drive on Windows 7.
If the unreadable CD-Rs still work in the old drive, then the problem is some difference between the old and new CD/DVD drives, probably in the laser used to read the disc.
On the other hand, if the CD-R is still unreadable in the old drive while running on Windows 7, then the problem is with the OS.
I think I had a similar problem when I upgraded from Windows XP to Windows 7. I don't remember if my burned CDs and DVDs wouldn't be recognized and just keep spinning, as in your situation, or if they would be recognized by Windows 7 but showed as being empty. The problem was the UDF support in Windows 7 and I should be able to find out how I fixed that.
Which software did you use to burn the unreadable CD-Rs and how did you create the CD-R? Was it the "drag-and-drop" method or did you open a CD burning app and burned an entire CD all at once?
Did you use the same software and method to burn the CD-Rs that are readable?