Hi,
On your old computer you'll need to Backup Files and Settings under Options and separately save all your puzzle files. Then reinstall on your new computer, and use Revert from backup file under Options to restore your files. I believe you need to do this (rather than just copy program files etc) because of the various entries in registry files etc. You'll then have to manually copy in your saved puzzle files.
I'm currently running version 9 and have saved the relevant installation files as a backup in case of system failure as these files are no longer available (since v10 was released) from the Crossword Compiler website. If you don't have them, and you are a licensed user, then you could try and contact the program's author who will probably recommend you upgrade but it's worth a try.
If you already have v10 the reinstallation process should be straightforward, I believe.
Best
David Stickley
www.stickler.com.au for free and printable weekly international cryptic crosswords