The starter being lowest componet in ski, probly has let some water get in there and has eventually gummed it up, and worn the two brushes. A kit is about $25 on eBay. If you hold the neg cable while cranking and it gets hot, most likely the wire at connection lugs are corroded. I've cut many lugs and soldered and marine heat shrank many cables over the years.
Keep your new battery tendered and always above 12.6v. Buy a tender, and a volt meter, and a pop-off tester, and a Metric tool set.
I recommend you change out the oil filter, and oil with BRP Synthetic oil, pull the rv cover with carb on it "as a unit",put the assy on your bench, the replace the two small oil lines from the oil pump to the 2 cover spigot tubes, flow test the oil pump and prime the lines, D/L a shop manual and read it, do an RV cover spec check (it should be 0.012") replace or machine if needed. Use new 0-ring.
ALL THIS before you ride it, besides the cleaning of the entire fuel system & carb rebuilding.
Then you will know what you have and respect this family gas sipper, for years.
I also recommend a ball valve in the large oil line down by battery, that goes to the RV lower cavity nipple.This is very handy when you store your ski, the oil pressure from the elevated tank does not push on the two center crank seals.
Keep grease on all the cables, its our friend and guards from corrosiveness & sticking.
Dielectrical grease is also paramount on all electrical connectors, fuses & holders.
Always gas up after riding, as the air can oxodateand ruin your fuel. Use Stabile if storeing more than two weeks, or over winter.
Check your water filter/separator periodically, dump it out to see if you bought water or contaminates. Keep grease on thesquare o-ring.
Put a glass marine fuel filter in the return line after the carb nipple. Once gas enters the circulatory system, it cycles thru the fuel valve, separator/filter, carbs, the returns to the fuel bafel chamber, them when gas is used, more enters in from the bafel lower screen/filter.
youtube does have merit.