If they are BOSCH solenoids, they could well stick anyway as they are crap.
A loud clicking says that the solenoid is getting power, but starter is not turning for some reason, the loud click is thr ring gear engaging as it does this just before the current is passed to the motor itself, ie PRE ENGAGED, the last part of travel of the solenoid is the CURRENT FEED to the motor itself, often when they(solenoids) jam it is the last part of the travel that is affected.
The easiest way to test is to take a live wire and a 50pence coin, with car on ramps and in NEUTRAL(!!) touch the live on the terminal where the solenoid feed goes to from the ignition switch, then if NOT turning bridge the TWO LARGE NUTS that are the main battery feed and the output to the motor itself from the solenoid, this is normally bridged internally by the piston in the solenoid that moves to perform these functions but sometimes gets stuck, a good clout often works as well.
Starters are easy to do DIY, so have a go yourself.
Other problems that occur are the bush in the engine end of the starter picks up and can jam solid stopping the starter, or there is a very large carbon build up in the contact area, that just needs GENTLY scraping out and maybe new brushes, there's really not a lot to them.
tabetha