How to restore this deck

I'd start by LIGHTLY power washing with a detergent, or if you don't want to rent a power washer and need a workout, use a stiff bristled scrub brush to scrub down the deck with detergent. That'll remove the black/slimy stuff, and will probably resolve most of the problems with the deck itself. Don't really grind into it with the power washer.

The main thing you're going to need to figure out before you can replace portions of it is precisely what the material is. Did your parents have the deck built, or was it there? If you can find old receipts or quotes, that might tell you what the material is. It also might be under warranty -- most of the early composites had a warranty for 15 or 30 years, and if it's only ten years old, then the spongy boards might be replaced by the manufacturer if they're still around. Hard to tell without actually having a product and manufacturer name.

The difficulty with replacing boards in a deck like this without exposed nails is that you have to take off most of the boards to get to the one you need to replace. You start at the edge and remove the facing board, and then you have to remove the hardware holding each board down in turn to be able to safely remove and slot in a replacement. The replacement also won't match, and unlike wood, the composites don't weather to the same color quickly. If the money's there, you might just consider having the entire deck resurfaced, especially if your parents are elderly and the house is going to be sold as they move on in life.

The jury is still out on these types of products. I was at a contractors day at my local Lowes and the rep from one of the manufactures of the epoxy style coverings was there demonstrating the product. The end result was a smooth, not sandy, but mottled non skid finish. the dried samples on display revealed about an 1/8" coating on the wood. I did spend a little time talking with the rep and he cautioned that the wood needs to be clean and free of any loose decay, oil or grease (like from a BBQ). Any loose nails should be replaced, better if the deck was screwed down so nails would not work up through the new finish. He did not claim that this was a "fix" for rotting wood or a surface in very bad condition. This product seems to me to be an alternative to conventional sealers or stain. The claim to fame is that it will outlast regular sealers and stain for years. The previous points about spacing and the top of the joists are very valid. My biggest concern is the holding ability if used over bad wood. I think lots of people will try this hoping to stretch the lives of aging decks. Since this product is so new, there are few anecdotal cases with which to compare it. I might be tempted to try if if a customer insists on it, but think I'll wait until I get some feedback from other contractors or users. the cost is also a consideration, it is expensive.