I was puzzed by "the one with the pin holes and a small square shaped socket" - I thought that referred to a single socket and I couldn't think if anything that looked like that. Some ancient proprietary thing, I thought. A DVI has a square section of four pins at one end hence my suggestion.

USB 'B' connectors are square. The monitor was described as old so probably not USB3 but you couldn't send video down USB 1 or 2 so it must do something else. If there were another USB socket it'd probably be a hub so you can plug in a mouse.

The make and model number would identify it - Dell apparantly fitten USB sockets.