Patch the laptop power cable

Duct tape fixes everything.

Properly, though? If you're adventurous and handy with a soldering iron, try replacing the internal power jack. You should be able to find a service manual for your model (via google) that describes the proper way to open the case.

Barring that, you'd have to talk to Dell about getting it fixed.

Yes. You can get USB power from another source but it still might not work...

USB power is only +5 volts DC. And as long as you don't connect the inner data lines (which can cause other problems) you should be just fine getting your +5VDC from somewhere else. But if this is an iPod or something then it probably still won't work. And the reason that it might fail is because some devices like iPods require a minimum amount of current as well as possibly even certain signals like a 1.5VDC level on a data line, for example.

Frankly, you'd probably be better off getting a powered USB hub. As long as you don't try to get an expensive hub, like for USB-3 or something, you probably can find one for under $20 or even under $10. So is it worth the potential damage to another computer over what might not even cost a saw buck?! (It's your decision...)