If your wireless router has multiple ports (it should), then you could disconnect your Modem (internet) and just hook up the 2 PC's. It will take a little configuring, but you should be able to transfer data between the 2 units.
One thing to think about...if you haven't backed up the data (20GB), burning it to DVD (should be able to get it w 5 DVDs) would allow you to transfer it to your PC, and keep a backup copy.
It's a little time consuming at first, but I took time to organize my stuff on separate DVDs so that when updates, new revisions., new romsets come out, I only need to "re-create" certain DVDs.
You could also look, into using your original PC hard drive (the one with the data), and "piggy-back" it in your new system. That way you have 2 hard drives in the new system. Then you can transfer the data (fastest way, especially with that much data), then when you're done, you can put the original drive, back into the original PC.
Let me know if you need any help with that last idea, it can be a little tricky if you've never done it before.

Good luck!