Stats, have you tried drying them out on top of the boiler ? the strips are sealed in some sort of laminate i think, the ballasts (they step 12vdc up to 110vdc) are hidden i think under the carpets in the ducting
Is the water actually between the laminate ? if not then why not try a multimeter on the ballasts ? then on the laminate strips ,if they work as well it could be something as simple as a fuse...
I know my illuminated sills are aftermarket, but it advises you to run the wires to the courtesy light fuse in the fusebox, i wonder if yours is the same ...
If you need to replace the strip, the sills on ebay ( i got mine from the US , landed for £80 for the pair ) the actual laminate strip is a block of colour rather than the cut out letters that you have there, you could put them under the old sills and it would shine through the cut out in the metal on the SL sills, no one would ever know, then sell the ebay sills on again, might work out cheaper .....
Hope this is some help .....