Did you perhaps plug the transceiver in upside down? This would result in a stuck receiver.

No, the mouse wouldn't work. It's possible the socket isn't centered in the hole in the laptop. Check this. If so, the plug may be off center and hung up at one side or the other. You would need to push the plug so it's centered to get it out. When I remove a USB plug, I generally put a finger on either side, press the fingers against the case and squeeze the two fingers together to ease the plug out. You may have to have the laptop serviced to get the plug out, as the socket may be defective. I don't know if Dell will service this under the warranty if it is still under warranty.