I love these intermittent glitches...not. Anyway the fuel cut solenoid is a gadget that protrudes from the side of the carby with a thick black wire with a single white stripe. It looks a little like a 'C' size battery (I know the codes describing batteries are different in some countries - they're also referred to as an R14) and it's job is to starve the carby of fuel after the engine is killed to prevent 'dieseling' or run on. But, seeming you've found out that it's an electrical glitch that is causing all your grief, all I have done is added a paragraph of irrelevant info. With the new ICM she should be running like a champ again