Without a little more info on your system and its use I am working blind .
Is it a TV system ,cctv ,radio??
In all cases test equipment is the usual approach.
However if its TV most systems have a central splitter/amp unit with
individual cables to each outlet.
If you have bad picture at all outlets suspect the splitter or feed to
it.(has the power been turned off to the amp?)
If only 1 outlet is poor suspect the coax or socket.
A simple (but not definitive) way to check coax is with a multimeter
.Disconnect both ends and check resistance between centre core and screen.
if there is no short then short one end together and meter the other end the
short should show.
This gives only an idea of the integrity of the cable (no shorts or breaks)
and will not show screen breakdown faults.
If cctv try each camera feed directly into the monitor bypassing any
recorder or again meter the coax .If you have BNC type couplings check the
centre pins they have a tendency to bend and even push into the plug when
forced onto a stubborn socket.
Others on this group may have better suggestions but for now