I would bet it is an earth loop.
First, nothing to do with earth loops but re terminate the BNC's at the back of the DVR if they are loosing signal when you move them. It is likely if the install is that bad, there are Loose strands of copper that may be shorting to the center core or the core is not crimped into the pin correctly.
Now get a earth loop isolator (about $80) and plug it in line with the coax in question to see if the fault goes away.
PS - is the test monitor a battery powered or 240v? I am guessing battery as this will lift the earth loop. The camera that works on the DVR but not the monitor may not have the shield connected but the earth is coming from another coax while connected to the DVR
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