Is there a way to extend an existing USB cord that cannot be removed?

yup, get a usb extender cable. For example:

http://www.usbgear.com/USB2_extension_Cable/usb-ex...

The link above is to show you what they look like (obviously you dont have to go for the 16 foot one pictured in the link above!! - I didnt even realise you could extend one that far - if you read further down the page it says you can daisy chain several of these to go up to 80 foot!!).

You can buy these from most compter stores or mail/internet order.

I use a small 50cm one, only cost me a few pounds, and leave it plugged in one end and the open end left on top of my desk - saves me from going down on my hands and knees and grope around the back of my pc when adding usb devices!

Hope this helps!

If there is a BIG LOTS in your area, they sell a USB extender kit.

This kit can extend any USB cable by 6 feet. The kit also contains adapters so you can change from A, B, mini-B etc, types.

Only $9.99, not including sales tax.