On the gelcoat: Faded/chalky gelcoat is generally oxidized. It's not shiny, may feel rough, and if it's a color it will look lighter than it should. To bring it back to shiny gelcoat, you generally* need to remove this top oxidized layer (and you have to have enough gelcoat left beneath it so you can expose a fresh layer without going through to the underlying fiberglass).
The variable is what you use to remove the layer, and how aggressive it is. Some "light" methods are a combined cleaner/wax type thing, or a very light-duty compound, or a fine-grit wetsanding paper (1000).
Medium methods are typically more aggressive compounds and/or more aggressive grit paper (600). Then there are really aggressive compounds and successively rougher grit papers.
All of the above are made by numerous companies. 3M, Meguiars, etc.
A plain wax is mostly just a protective layer (not that there's anything wrong with that - UV protection especially is good), so I think of it as something I put on after I have the boat looking how I want it - not as something that will "bring back" a finish.
So... I would start with a less-aggressive method and see how that goes, and then progressively move to the more aggressive ones until you find the one that works. Then step back down "through the grits," so to speak, polishing it ever finer, until you are back to where you want it, then wax.
(This assumes you've started with a clean boat.)
Sunbeam
*There are other/new methods that, as I understand them, sort of "fill in the rough surfaces" to make them look shinier (Poliglo, floor wax, etc.). I'm not experienced with those.