Roll starting (jump starting, as we used to call it) will only turn the engine and cause it to start as if the starter was turning the flywheel...
So, no...it won't turn the starter...but if you try rapping on the top part of the starter (not the bigger body, but the little thing on top....that is where the plunger is detonated to cause much booming...(as my friend in the ESP class describes it)...
To jump the solenoid, you need to put a screw driver between the two posts on the solenoid...but be careful...too much heat on the centre plastic will cause it to crack...but at least they're fairly inexpensive to replace...
Oh...there should be a small boot on one of the terminals...make sure that is tight...it has caused my starter to fail...but did not affect the lights...so you've probably got a combination of poor ground and dirty terminals...
Tighten the ground wire that goes from the battery to the starter...that is most likely your problem right there...