There are two things to try:
1. When it asks for the CD to authorize it, eject your Logic CD with the CD-ROM's eject button after allowing it to spin for 15-20 seconds. Sometimes this gets the job done but will quit before it crashes.
2. Go to your c:\windows\system directory, move aspienum.vxd to the recycle bin (don't throw the file away by deleting it) and run Logic again, try to authorize it. If successful, replace the file to its original location.
3. Try a combination of both if it still doesn't work- move the file and then when authorizing, eject the CD.