How I check a solenoid - shake real hard so that the center of the solenoid can move. If you do not feel a movement in the solenoid, I do not use it.
how a solenoid work see link
also are you leaving the switch for long periods of time? if so the fuse might be the problem. If the fuse get hot it will short out.
note the second post that larrybl has for testing a switch - is is for a magneto switch
a battery switch has the S in the position that M is.
the 110 series manual - section 40 electrical section will answer most of your question