The socket you should be trying is the blue socket that has 15 pins, and it's near to the keyboard, mouse and several USB sockets.
See photo. Note there is another similar blue socket lower down, that's the 'AGP' or 'PCI' graphic card.
It's fairly common for the PC to make the lower one active, if a graphic card is fitted there. If there is no card in the lower position, the upper one will be used, known as 'on-board' or 'integrated graphics'.
You may need to make a change to the BIOS settings also.
Try the other socket for your monitor lead first though.