I think it a good idea if we start at the beginning. There are three main parts to video editing.
1. Capture
2. Editing
3. Authoring (Converting to final video, DVD etc.)

The preferred method of capture from a DV camcorder is Firewire. Capturing via a USB connection with something like Eazycap can and probably will lead to all sorts of problems in the editing and authoring stages.
You say you fitted a Firewire card!
Did you take the appropriate static electricity precautions before tinkering with the innards of your PC?
Are you absolutely certain that your card is Windows 7 compatible. Many of the cheaper cards are NOT. Did the card come with a instructions on the connection procedure. It is important to open your software and turn the camcorder on in the correct sequence otherwise the camcorder wil not be recognised!
Whilst you are looking at the above go to one of the clips you have downloaded and just double click on it. Your default player should auto play the clip. If it is showing the letterbox borders then the chances are the capture was at fault. This happens a lot with USB connections.
All this looks a bit daunting. Video editing is one of the most demanding processes you can take on both in terms of PC resources and your patience but it is well worth pursuing.
You are lucky, you have potentially the very best setup. A good camera and a Firewire connection that will probably download to the AVI format which is acknowledged as the easiest and most reliable format to edit, so success is just around the corner.
Final bit of advice, forget using the USB connection, concentrate on getting the firewire working. You won't regret it, guaranteed.
Check with any good Forum dealing with Video Editing and I'm sure this will be confirmed amongst the real and acknowledged experts!
More help here whenever you are ready