Chances are good it runs if you clean the motor brushes, armature, and shine the wheel treads some. May take some lube and friction at the axles to re-establish electrical contact too, but the Marx motors want to run.
The key to washing is drying it quickly, before oxidation can set in. I've literally dunked whole engines, and the rolling stock. I dry with a towel, then a hairdrier, sometimes I use forced air from a compressor too (especially on motors) then I re-lube. "Painting" a thin layer of oil on any raw metal till it darkens slightly letting me know it's covered.
Another example-- My window fan motors also get washed. With the garden hose or shower-head and are then left to dry in the sun, then another day or two indoors. Dirt and dust jammed inside the motor is the #1 reason those fail.
The white spots may just be mineral deposits, but could also be mold growing in the paint. Keep an eye for the next year or so for a re-bloom. Finish restorers usually do a good job of killing mold if its not too deep (I've used kerosene on a rag to kill it on a few toys in the past) (test chemicals first!)
There are automotive cleaning waxes to be considered too. Basically very light rubbing compounds. I've use them often, even on brand new, 1 day old cars to clarify the clear coat even further. I always liked Meguiar's Mirror Glaze #2 a fine cut cleaner.
Till I could read off the reverse reflection of the bottle sitting on the ground 
