That white powder is from moisture corrosion. It is blocking some of the current to the plugs. Scrape it off. Also, check the center carbon button. When the powder blocks the voltage, it backfeeds into the button and can burn it off in the cap. There is a silicone washer and a spring under a cover that the button comes out of. Remove the rotor too and see if the backfeed has burned thru to the shaft.
AND while you have the cap off, check the 2 little wires coming out of the pick up coil. They get brittle and break when the advance moves. They cause intermittent running issues and false starts.