this sounds as if you are not getting gas to the burner, ok pilot light on, so gas to boiler, But it is not switching the gas to full burner. Cheap, probably not that cheap, you need to get someone that knows.
Without doing a series of checks, difficult to say where fault lies, you say primary flow is ok, But is it? might seem to operate, But does it? As you have gone as far as you are able, get someone in, expensive I know, But what choice?
SD, June 2011