How to transfer files when USB is busted

I thought I'd ask this here in case anyone might know a solution.

For some reason the USB ports on our old computer have stopped working. I'd like to copy a bunch of it's files off it (preferably without removing the hard drive at this point as I'm not tech savy and have doubts I'll be able to put it back in). The wireless router (right word?), seperate from the computer, still works and has a cable running from it to the comp. I was wondering if there was some way to send files wirelessly to my laptop (who's usb's still work) and save stuff to a memory stick?

Any ideas?

Dropbox.

Fair idea. Any way around using a USB port, so I don't use up my data limit?

As alternatives you could try simply burning the files onto CD / DVD. But if you've got too much data for that then you could set up a home network and just drag/drop the files between your computers. There are various free programs that can assist you in doing this, but I've never tried any of them - DropBox provides an online backup as well as a transfer means, and the windows home network is very easy to set up.