Why is my spacebar stuck, even when I unplug the keyboard?

My Dad's keyboard is acting like the space bar is stuck. I thought it might just be the keyboard going bad (it's fairly old Dell KB216 Wired) but even when I unplug the keyboard from the PC it's still like the spacebar is stuck when I'm in any field where typing is available.

My first instinct was just to buy a new keyboard but if it's having the issue without a keyboard plugged in I'm not sure if something else is going on.

Any suggestions would be appreciated.