First thing i would do is to grab a low volt meter and connect one lead to negative the other one to positive terminal on the battery , Then start the jet ski and see if you are getting a reading less than 13 volts = Bad Rectifier ,bad magneto. Or bad cable connection, Follow the 3 yellow wires from your rectifier to the triple connector coming from the engine (Magneto) if it checks out good, Do a search on how to check a rectifier , Much easier buy el cheapo from flebay and see if that work !! If it does discarded and buy OEM from this site or any other site but make sure its OEM.
PS..check charging 30A fuse on fuse box.