No, do everything on the NEW computer. Run the program, go to the menu. Select Help > About Poker Tracker. A window will open. Send the product ID from that window on the support ticket. Then do the steps in the FAQ link.
OK, the format is not even close to what PTS looks for, but depending on how many hands you have you could open the files in Notepad and replace the first line of every hand so that it goes from this: Full Tilt Poker Game #28301988378: Table Edith - $2/$4 Ante $0.40 - Limit Stud H/L - 09:44:55 EET -...