If you can install the game juts fine on your laptop, why are you worried about installing it on your desktop?
Take the installed EQ folder from your laptop and copy/paste it onto your desktop with a USB drive. No need to run the install utility more than once.
Your processor version won't matter for EQ, I'm playing on a Sandy Bridge 3570k and running just fine in Ubuntu 12.10-64bit LTS via Wine.
Have you tried NOT using compatibility mode?
Try this for me, let me know where you get hung up:
1) Copy your
default Titanium install directory from your laptop to a USB drive (C:\Program Files\Everquest or something like that, copy the WHOLE Everquest folder).
2) Paste the Titanium install onto your C: drive on your desktop. Make sure you have read/write permissions in the Everquest folder.
3) Update the default Titanium install with the P99 specific files. Follow the
getting started guide.
4) Run P99.