Just a couple of things on this....
These boards have an eps foam core.
In this the foam is extremely light - it has to be, for it's a big board and there is a lot of reinforcement on heels and finboxes so weight reduction is V important. The Sectors are not as light as they could be, but they are very strong... The fact that they are EPS cores will make them absorb water and will also make them reactive to polyester resin when breached... So, please don't expose the core to polyesters.. (includes solarez). Repairs MUST be done with epoxy. That said EPS is functionally far superior for bigger volume boards.
While it is possible to crack the paint and not the laminate I would strongly suggest that if you see any cracks or bruising to the skin, pucker up, get your lips on there, and if you can suck air out, then water can get in, so get it fixed.
Before I started Kiting in '98 we had been using EPS cores in windsurfing since the late 80's. It's possible to get the boards to delaminate, but the water has to be in there for some time, and the eps will soak up a lot. If you think there is water in there, before you repair, open a small section of foam to the atmos, leave it propped in a warm dry room with the foam at the base to let gravity take the most out. After that put some toilet paper in, wound up as a wick, with the end fanned out to wick and evaporate the water away. Putting a dehumidifier in the same room for 3-4 days will help wick it all out.
After that, repair with epoxies and you should have no problems... But check your board every once in a while, and do treat them with care. They are strong but sharp hard objects are not it's friend...
When you go through the white paint you will first find a black carbon wrap, after that you will either hit eps on the deck, or if around a fin box you will find a non absorbent pvc foam called airex. This may be your brown stuff.. it does come in different colours, but you'll have to do some digging and sanding to find it.
I have seen many windsurfers back in the late 90's strapped to spinning devices (there was one in south africa). Made from a washing motor strapped to a spinning car hub welded into a frame, you strapped your board to it and span it like a top. It would take 4-5 litres of water out of a sodden board, quite incredible, but the fact that the boards broke loose regularly made it a risky proposition. Like medieval medicine, this was kill or cure, and plenty of people went home with their favourite boards in bin bags.