I think you can repair the solenid yourself possibly. I have repaired many Chevrolet solenoids by using the following method...
This is a maybe solution because I have not had a reason to date to remove and see if I could repair a Suzuki solenoid. I am guessing the can be repaired in the following manner since it is coommon and Chevrolet did market some Suzuki's under their name.
If you can remove the cap on the solenoid inside you will find a plunger shaft with a round disc on the end that resembles a big washer. Remove the keeper that holds the disc in place and filp the disc over. If you can't flip it over then sand it down and put it back in place.
The disc oxidizes or becomes pitted and doen't make good contact when engaged. This is the most common reason for failure. If this does work please let me know. I have suggested this before and asked for a return response but to date have not hear back by reply.
Thanks & good luck! Tux...