Intermittent non-start problem (help!)

Appreciate any experienced advice.. here's my problem:

2004 Neon sxt, manual transmission. Have had this intermittent problem for a long time (couple yrs). It was my teenage sons car. I've done everything common sense related for being.. not an expert, but generally familiar with autos.

When turning key to crank, all lights/power work, but engine doesn't do anything. It's completely random, and -usually- works after I mess with it for awhile (pump clutch, repeated turning key to crank etc.), but nothing seems consistent or common. Am I correct that it could be:

-starting relay is intermittent
-clutch safety switch has a problem
or..
-can a starter intermittently work?

The answer is any or all of the above. Loose connections to the relay, ignition switch starter motor, the list goes on... It's a Neon; electrical issues are part of the package.