Without looking up the standard my assumption (a dangerous word) would be there should be a 5V TTL signal on the port and it shouldn't be distorted much when the monitor is plugged in.
If you have a scope, have a look at the back of the sync input socket, or the equivalent pin of a multiway socket.
If there is a signal, & it looks correct, the connector, cable, & display adaptor is ok.
You should be able to trace either a cable, or if it directly connects to the PCB, the track which runs from that point.(often, if a cable is used, it connects to the PCB, so you will end up following a track, anyway).
There may be a dry joint, or other disconnection--------if so, the signal will either disappear, or become reduced in amplitude.
If that hasn't happened, you can then probe around the device it ends up connected to.
If this is an unidentified IC, take note of the type number, then Google for it, as these often show typical circuits using the device.
Many of these monitors are fairly generic, so it also may be possible to find the schematic of a similar one.