Try a spray on teflon dry lube for sliding mech's from milk cars to gatemen shacks. (T-9 is great though pricy if it's still around, but I'm ready for another can ($18 at Grainger about 2004)... the cheaper autostore brands aren't awful) It will dry fast to a very very thin waxy looking coating; slick as Elvis 
Wet lubes can actually be too sticky for small parts. Breaking free of it's grip to slide at all can upset the balance of spring loadings etc.
It won't migrate, plastic safe, people safe (T-9 at least) cleans of hands. It is a lube and deicer for airplane wings and flaps but works great with small stuff too.
Do you have a meter? A test light/probe? . Start by insuring there is no contact from frame to either wire or coil terminal to chassis BY METER or TESTER. If that reads no continuity by whatever method you use, now measure the coil ohms. Checking for no continuity to frame ensures a true reading of the coil.
There will be an inner sleeve for the slug to slide on. It may be worn or even melted. Feel as it slides for evenness and hanging; the effect of a worn one is surprising. (most solinoids like T-9 here. It would often help me with nearly dead pinball coils last until new sleeves arrived, and extended the life of new)
Your own fingers should also be able to tell if that electromagnet (coil) has a good pull or not.
Coil wire is coated with a "paint" (epoxy mostly, sometimes lacquers though). The coating may crack, burn, be washed off/thin by loose solvent drops, etc...or wear through from vibration (there is a 60hz buzz every time it works, heard or not) Depending on where/how it shorts inside decides if the pull is slightly or greatly weakened as a short basically removes X wire turns. (More wire turns added =more pull).
