@Rubens,
A single key malfunctioning, and eventually stopping entirely, is definitely a sign that you have something going on with the rubber dome cap--either grease/dust that is blocking the contact, a worn out conductive pad on the sensor, or more seriously, something wrong with the contact on the circuit-board side.
Cleaning the contacts is a very good first step approach, and ANY knowledgeable or beginner DP tech should be able to do this. In fact, you could easily do this yourself if you don't mind going through the hassle of disassembling the DP (maybe you don't want to bother with that, which is fine).
Also, Kawai US is very good about sending replacement parts and service manuals (they sent me the service manual for the MP-11 and the NV-10 when I emailed to ask, no charge). They'll give you a price list and directly sell you replacement rubber cap strips so long as they have them in stock, too.
So if you're looking to save as much money as possible, I'd say definitely try to clean the contact area around the dome cap for the busted key and see if that works. If you want to avoid possibly needing to open the piano up again multiple times if that doesn't fix the problem, just get a complete set of dome cap strips from Kawai, and change the whole set out for all 88 keys.