Welcome to the forums. There is no check for a CDI, other than replacing it with a known good one. My guess would be that the CDI is bad, because that is a pretty common part to go bad on the Fourtrax 300. I would start by testing the ignition coil, first. Here are the procedures for checking the ignition coil, but this is from the 1995-2000 Fourtax 300 service manual. It should be the same as the '88, though.