Ah work pc..
You may need to move the files to your My Documents on the first pc so you can transfer them to the new pc.
Then if you haven't already done so, right click (or left if you're left handed) on the My Documents folder and set it to share.
Just incase the two computers haven't been on the same network before of if one swaps netowrks, connect them to the same one while both are off.
Then when you turn them on one at a time they should see each other and be able to transfer the files. If by some reason they won't talk try running home network wizard.
If the are set to talk to different network names that would an issue. So if the home pc is set to look for Home network and the work pc is set to look for the Work network, while they may be able to see each other they won't share with each other.
Also, make sure both the computers don't have the same name.
Hope that helps you out.