some starters can be "tricky" when putting the brushes in ,if you have any problems i can always take mine apart to instruct you. The problems with solenoids can be many, it is best to start with checking the current to the the coil (from the start switch) with too little current the solenoid will not pull in or just chatter like a dead battery. you can jumper it direct to the battery and measure the current with a meter then compare it to the measurement thru the st. switch.
OR- the contacts to the starter may be burned or dirty, if water gets in this will gunk up the contacts. In the bad old days we us to take it apart and flip the contact washer over and file the brass bolt heads.
OR- the wire/connectors to the starter may faulty replace it anyway if it's old,~ cheap~ and easy.
good luck Rob