98 Chevy Blazer (2dr) won't start without first messing with the negative battery cable?

I am having intermittent trouble starting it. It will just click. The battery is charged and powers the rest of the vehicle, but I have to manipulate the negative battery cable for up to a half hour before the engine will turn over. I was recently told what a solenoid is. Could this be faulty and only work sometimes? And how would messing with the negative battery cable make the truck turn over? Also, I am unable to locate the solenoid. Is it directly underneath the battery? I haven't looked there yet. Thanks for any help you might provide.