Yes leejxxxxx ..... I agree. No jumping. Try another battery first.
Yes a solenoid on the starter will corrode as well as the connection.
I agree that bad solenoid contacts will cause this condition. Again a good smack might make it contact. Of course a replacement is in order. You might be able to replace just the solenoid / relay part. I always take the time to seal the covers with RTV and coat the cable / wire connection with paint RTV or something. This area is exposed to the elements