I think the best way to do it is to use your Router. In case you don't know how to do it, I will write it down step by step. (I am bored right now anyways =D )
Step A:
1) Go to Control Panel
2) Open Network Setup Wizard
3) Choose the following buttons: Next, Next, Next (Yes, use the existing blah blah blah), Next (Computer name, etc), Next (Workgroup), Next (Turn on), Next, Next, Next (Just finish) And then restart your computer.
Do step A for your laptop and for your computer you want to format
Step B
1) Choose a folder in your laptop that you want to use to store the files from your desktop.
2) Right Click
3) Property
4) Sharing
5) Select "Share this file on network" and "Allow users to modify my file"
Now go to your desktop
Step C
1) Open any folder
2) Type in //nameofyourLaptop
3) Chose the folder that you shared from your laptop
4) Move whatever files you want from your desktop into your laptop
After that, everything else should be self explanatory.
I hope that help. =]