G'day,
i highly doubt the solenoid would have been damaged when jump starting it unless you shouted it out somehow. the easiest way to test it is to locate the smaller of the 3 wires (generally comes from somewhere in the dash) jump that one to the live terminal (battery side) of the solenoid. if the solenoid 'clicks' and the engine spins it indicates that it is very unlikely to be the problem, unless its some sort of freak intermittent fault with it. when doing that test be very careful that there is no possibility that sparks generated could cause a fire or damage of any type.
i know it may seem fairly obvious but also take off all the lugs from the solenoid, battery and starter motor and wire brush them clean to make sure they are perfectly conductive.
see how these tests run
regards jay
