hi, my name is XXXXX XXXXX I will help you ..
ok, the solenoid is part of the starter ,so that being said ,you have to check to see if you are getting a 12 volt signal to the solenoid from the ignition ,that is on the smaller wire check for a 12 volts while the key is turned to the crank position ,if you have that and 12 volts on the bigger wire then the starter is the issue ,
you may get lucky if you let the starter dry out ,then bench test it with 12 volts to where the bigger wire went and use the casing for the ground ..
then using a small screwdriver ,with the screwdriver touching where the bigger cable went also touch the end of the screwdriver to where the smaller wire went to ..
if the start still doesnt kick out good then replace the starter .
or you can just buy a new starter ,that is up to you..
I would at least let the lod starter dry out and then try it ,most times the starter will be ok ,but sometimes it wont ..
or you can take out the starter and have a parts store check it out for you ..