Can I transfer my existing profile (library) to the new install? Please tell me I can. And if so, how?
Absolutely.
MC includes a Library Backup feature. They happen automatically, in fact, but you can "force it" by going to File > Library > Backup.
The Library Backup contains the entire MC Library (the database, not the media files), and also all of the settings for MC. So, when you get your new machine set up, you'll just want to:
1. Make a backup of the Library in MC on the old PC. Save it with your media files.
2. Move all of your media files over to the new PC, and the new backup you just made.
3. Install the then-current build of MC and get it registered.
4. Restore the backup on the new copy of MC.
So long as the media files are in the same "place" on the new machine as they were on the old machine (still on F:\ in your case, if I remember right), then you'll be instantly right back where you were!