"Every now and then it won't start after turning the key for a few secs. So I turn it back for several seconds. Then start it again and the engine struggles at low rpm and I have to give it a bit of gas to get it idling normally. This sometimes happens when the car has been left for a short period if time like 15 mins and less often when starting from cold. Could this be linked to the solenoid problem?"
This could be the ECU temp sensor relay, sounds the same as the problem on my 8V GTI. Relay is about £12.