Alternately, if you can't afford a cable tester, you can buy or build a cheap continuity tester or borrow a volt meter (digital or analog).
Example of testing cables with a cable tester and a meter:
(one problem with this example is that he does not test for shorts. Remedy: take the same probe to the remaining pins to be sure it does not zero on pins the signal is not suppose to be present on.)
Example of home made continuity tester:
If you know that your cable has continuity (no opens) and no shorts, then you might still be scratching your head about noise issues. Line noise can have many sources:
1) ground loops, there are a ton of ways to have ground loops, here are few that come to mind: multiple and inconsistent ground sources, outlets not grounded properly, faulty ground connection inside your equipment...
2) proximity issues, placing a cable too close to a power field especially if the power is unbalanced and the audio cable does not have very good shielding will make things worse.
3) cable integrity, compare a good shielded cable with a poor one, this should convince you to test and compare cables when you are purchasing replacements.
4) utility line noise: Sometimes it's not your equipment or your cables. If you have an O'scope take a look at the AC coming out of the wall at the gig. If you see huge spikes moving through the AC it may be from that guy welding next door, or some other source in the neighborhood, or even the fluorescent lights at the gig or a bad ballast, or light dimmers that use SCR's. You might consider a line filter/power conditioner to clean this up.