Personally I would fit a new solenoid for no other reason than I dislike the sticky staining of WD40, but then I have a particular hatred of the stuff. It would be worth first testing the fuse and electrical supply if you can.
You may already be aware that WD40 is not, and was never designed to be, a lubricant. It was the result of many tests of various mixtures whose purpose was to drive water from the surface of wet steel in order to prevent rusting. The winning mixture was the fortieth mix tried, hence WD (water displacement) 40. It's true that it contains a mineral oil, but the MSDS reveals it also contains an organic solvent similar to paraffin and a perfume to cover the stink of that paraffin. As the solvent evaporates it leaves the oil and the perfume residue which, as I mentioned earlier, leaves a nasty sticky mess.