Drain the carburetors (one at a time) into a clean cup to see what comes out.
Any foreign debris - clean the carburetors and inspect the inside of the fuel tank for rust.
Is it a 1986 model by any chance? If so, check to see if the igniter was ever changed. I don't know the part number of orginal and defective igniter used on the first year bikes, but American Voyagers Association should be able to help, check their website. The flawed igniter had an electronic ignition advance problem that was fixed on '87 and later models.
