200 CDs? That is nearly 140gbs of space.
If you have a spare SATA connector on the MB, you should be able to hook up the old HD with a SATA -> ATA adapter (Abit makes one). Try going to a local PC shop and getting a regular IDE cable for your HD and see if those work instead. I don't know if Dell uses some properitary format for their IDE cables. If for some reason, that doesn't work, you can always hook up the HDD to another computer, and connect them together on a network, then just transfer the data over.
If you had a DVD burner, that might not be a bad choice if you can cut down on some of the stuff you want to transfer. Shouldn't take more than a couple, considering they take 4.7gb each (or even 9.4gb if you have a dual layer burner).
Personally, I'd try hooking it up to a another computer, then just transfer everything over a network. Assuming they are on a LAN, you can easily transfer at rates of 5-6mbps, or probally even higher (havn't done it in a while). It might take a little while to transfer that much, but it should work flawlessly.