Check for continuity between the corresponding pins of the 15 pin VGA connector and the wires inside the monitor. The pinout of the connector is available here:
https://en.wikipedia.org/wiki/VGA_connector
In particular, you want to see that pins 1 and 6 are continuous through the cable. if you look at the cable end inside the monitor, you will likely see 3 coaxial cables for the RGB signals (and maybe 2 more for sync).
Obviously, you do all this with the monitor unplugged from power.