If you're synching FeedDemon with Google Reader, simply install FeedDemon on your new computer and give it your Google login. FeedDemon will then show the same feeds, starred items, tags and shared items that were on your old computer.
If you're not synching with Google Reader, copy FeedDemon's cache folder (File > Manage Cache) from the original computer to your new system, then make sure that FeedDemon on your new system is pointing to the correct cache folder.
