Your solenoid could be bad also. If you have removed and cleaned all the battery terminals and checked all connections for tightness, charged the battery (check that it isnt still malfunctioning as they occassionally die on the vine so to speak and wont take a charge) then your are left with starter, solenoid or switch problems.
Recently my B.I.L.'s Dodge truck had battery problems that would do just what yours is doing, jump it and it would crank and check good, then just click next time. It took 2 trips to the dealer to replace the battery and then only after it finally shorted completely and wouldnt charge or click the solenoid. Sometimes batteries develop internal shorts and check normal when the broken terminal is grounded then it short circuits and wont work at all. Short circuits are hard to find expecially intermittent ones.