Hey there Tigersand,
If all you are using the old desktop for is storage, all you need is the hard drive. You could take it from your old desktop and just plug in and install it onto your new desktop. I'm guessing the operating system is still all on it, but you could format it and have all the free space(backing up and taking any files you want to keep first of course). If you need info on how to do this, Troy's How To Build Your Own Computer guide
shows how to install a hard drive, about halfway down. It's quite simple, you just need to plug in a power and communications cable. Lock it into place with a few screws as well. There should be an empty slot to put it in.
If you need further help, or this idea just doesn't fit for you - just say so
Hope this helps,