Connect Mac to an external display
Those specifications and those of the cable and monitor indicate that it should work.

You could try resetting the SMC on that Mac by shutting down the Mac holding down the Shift+Control+Option keys and the Power button at the same time. Wait 15 sec and then turn it back on.

Failing that you could start in Safe Mode by holding the shift key while booting (booting will take a lot longer) and try plugging in the monitor then.

Failing those I would try another adapter, preferably one with an all digital signal path like a Mini Displayport to HDMI or DVI-D