If your still within the 6 months since you purchased Pro, enter the e-mail address you used to buy it here:
http://sales.limewire.com/support/pro_lookup.php, and it'll take you to your personal download page.
If it's past the 6 months, you'll need to transfer the program from your old computer to your new one. You can do that by copying it to a disc and loading it from there, or try the instructions in this thread:
HELP!! Tunes to new pc.
If all else fails, you can still d/load the free version from here:
http://www.limewire.com/english/content/download.shtml