Networking is your best shot. FTP is just an extra step and would actually take longer to transfer the files. Once your 2 computers are networked together (which it sounds like they already are). Just go into Explorer and right click on a directory that you want to share and choose the option to Share it.
Then you can always browse the network on your other PC and find it browsing through the network.
Or just go to your new computer and go to run and type \\enter old computer name here \enter the name of the shared directory here
<a href=\"http://www.technogab.com\">Technogab Podcast</a>
<a href=\"http://phobos.apple.com/WebObjects/MZStore.woa/wa/viewPodcast?id=196334747\">Subscribe via Itunes</a>
<a href=\"http://feeds.feedburner.com/technogab/feed\"><img src=\"http://feeds.feedburner.com/technogab/feed.gif\" style=\"border:0\" alt=\"TechnoGab Podcast\"/></a>