Barrbender has a new PC and a transfer cable for migrating files from the old computer. But he has one problem: He didn't buy a new monitor, and therefore can't run the two PCs simultaneously.
If you only have one monitor, a transfer cable isn't a good option. Neither is a network. I see four options for you. Any one of them should work.
1) Copy your files from the old computer to an external hard drive and sneakernet them to the new PC. This takes longer than using a cable or network, since you basically have to transfer everything twice. But you don't have to sit there and watch it happen; you can get up and do something else while the first transfer is happening, then again for the second one. Windows Easy Transfer (the transfer program that comes with Windows 7) supports this technique.
2) You can remove the hard drive from the older computer and install it into the new one as secondary "slave" drive, and do the transfer entirely in the new computer.
3) If you're not comfortable opening up your PC, you can buy a SATA-USB adapter (they cost about $20) to turn the hard drive from the older PC temporarily into an external hard drive you can plug into the new one.
4) You can borrow another monitor.
Contributing Editor Lincoln Spector writes about technology and cinema. Email your tech questions to him at email@example.com, or post them to a community of helpful folks on the PCW Answer Line forum. Follow Lincoln on Twitter.