ummm i'm not quite sure if this will work... but here goes...
1. take the torrent file and the files downloaded from it on a portable diosk and transfer to the new PC
2. open the torrent file in BitComet and shift the downloaded files to the specified directory
3. if it asks for hash checking, click ok and let it continue and it should probably start seeding or downloading from wherever it stopped
do let me know if it works... :)
cheers