I'm not familiar with your exact sled, but when it's not charging, you either have a bad stator, or a bad R/R (rectifier/regulator)....which converts the unregulated AC from the stator into DC limited to ~14v.
On newer Cat EFI's, the R/R is built into the ECU, all it powers is the fuel pump and power valve servo.
Looking at the parts picture for your sled, you have a separate R/R unit (part #1 on this
picture). That's good, easy to replace. Probably has either four or five wires....three are the same color and go to the stator, there may be one +12v output and the ground is through the mount, or it may ground through a -12v wire. Problem is these are kind of tough to test reliably.
The good news is that R/R's are extremely generic. They all do exactly the same thing and are totally interchangeable between manufacturers, machines, brands, ect. One from a Honda jet-ski would swap with one off a Harley, the only differences are typically in size/shape. Hop on ebay and find one on the cheap. When the one on my bike took a dump, Yamaha wanted $120 for a new one, I got a used one off a Ninja ZX14 for $20 shipped and it worked fine(albeit mounting it in a different spot since it was a bit bigger).
Older machines (say pre-2000) typically used shunt-style R/Rs, which all fail eventually. If there's a part# on the unit, if it starts with "SH" it's a shunt. Replace it. Newer ones start with "FH", meaning it is a MOSFET style, which are much more efficient and reliable. They're completely interchangeable.
This isn't a direct application, but much of the ideas are the same, here's
a write up I did for a bike I used to own.