I know this might be a stupid suggestion. As I am no plumber, and besides you may have already done this.
Switch the broken radiator ( lounge) for a good one ( kitchen). Then check to see if the problem persists, if it does then obviously it would mean there is a problem with piping.
And if it is 100% not working then I am not sure on how to fix, possibly replace if not expensive? From somewhere like Screwfix?
Sorry not much help I know. but hey.