Strongly suspect a the USB controller chip is fried
Is it still under warranty? If so, time to call in as its not realistcally repairable - unless you can fit a USB expansion port into a PCMCIA port or similar (I've not checked the spec so don't know)
Just in case its a software gltich (and Dell will expect you to try this anyway) try restoring the machine back to factory settings, just to prove the point that it is a hardware problem
Make sure you backup first!
My thoughts? The cable you used was faulty, shorted and caused a burn out. You're lucky the ipad still works