It would seem that the plunger on the left is stuck in the solenoid coil; it may be possible to free it up with a spray of PB Blaster. The wig-wag assembly (also called the 'control magnet assembly' in older WP/Kenmore repair guides) may be replaced if necessary. Not sure of a current part number but I am sure other more knowledgeable folks here will chime in with that.
The good news - swapping out a wig-wag is not difficult. Even I have done it... LOL
IF the plunger itself is broken or damaged, a replacement is available (I have that part number and a picture if you need it).