A locked on coil is more than likely the result of a dead transistor on your driver board. I dont have a space station manual. If you have the manual it will tell you which transistor is responsible for switching that coil.
With power off, use a multimeter from the outside legs to the centre and compare with the one next to it, if it shows a short circuit or is different from the working one it is faulty.

Raysco is spot on. All the coils are controlled on and off by switching transistors that act exactly like solid state relays.

The one that drives the sling that is locked on will be shorted and so it is unable to "turn off". This is possibly the result of the diode on that coil being faulty as that would allow huge voltage spikes to travel back to the transistor and damage it. This is the reason it is VERY important that every coil has this "snubber" diode fitted.

Fuses are only there to stop the machine catching fire and burning your house down - they ARE NOT there to protect the machine.

As Raysco says, you should investigate the schematic and identify which transistor is the cuprit and measure it BEFORE replacing. Also confirm that you have installed the replacement diode on the coil the correct way around or you will have more problems.

It is also possible the coil has been cooked if it was latched on for more than a minute or so??? Make sure the plunger moves freely inside the coil sleeve.

Read and do your homework BEFORE diving in and grabbing the soldering iron as 30 minutes preparation will mean you should be able to effect the repair in five minutes.

If you look at page 2 of the manual, the solenoid table shows you that the right sling is special solenoid #4. If you follow this to the right it also shows you that Q69 controls this coil. When a coil locks like this the Tip 122 is shorted, also the predriver and diode have been stressed and need to be replaced. If you left the power on to long the coil will need to be replaced also. When all of this has been repaired, there still maybe the original problem that caused the coil to lock in the first place.