C1 Central Locking and Starting Issue

I had a similar headache with my C1. Same symptoms - central locking going haywire, engine start issues. It's likely the radio antenna amplifier. In the case of a broken antenna, the car radio's reception will be bad.

Could you elaborate on where exactly I should be looking for this radio antenna amplifier and how you pinpointed it as the culprit?

For me it was the bumper antenna. Unfortunately, it's a known weak point. Take it to your local workshop. I'd advise against attempting a fix yourself, you might screw up something else, which is going to be even more expensive. The mechanic should be able to test the antenna and its connections. It cost me 95€ to get it replaced, so at least you know what to expect.

I appreciate the insight. I'll take it to a shop and have them check the antenna and connections, like you suggested. I was quoted 95€ for the antenna replacement, which corresponds to your experience.