The ignition system is the points, condenser, coil, distributor and spark plugs, the parts that supply the spark that "ignites" the fuel. The ignition system has nothing to do with the solenoid or the starter.
The key switch controls multiple circuits. One is the ignition circuit and another is the starter circuit.
The fact that the key doesn't turn anything on or even cause the solenoid to click indicates that either you have a bad connection before or after the key switch or the key switch is bad.
The other symptom, of being hard to get the starter to engage the flywheel when you jump the solenoid could be a few things as well. First make sure that the cables from the battery to the solenoid and from the solenoid to he starter are good and the connections at both ends of both cables are clean and shiny and are connected tight, and also make sure that the ground cable from the battery is good and has clean bright connections at both ends as well, plus make sure that the battery itself is good (take it to an auto parts store and get it tested if you don't have the ability to test it yourself, it's free at most good parts stores) and fully charged and then see if the starter engages better.
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