I am unable to receive any more minutemen quests after The Castle.

I was unable to complete Taking Independence because there was no one left after the battle to man the radio station.

After reloading saves among other things, the problem wouldn't go away.

I used the console to finish the quest.

Even so, Preston won't give any further quests, so I can't begin Old Guns.

Already sent support ticket to Bethesda support and no response yet.

Advice?

I know for BoS line I had to complete the main story to a certain point. Could it be the case here too?

Preston Garvey is bugged at the present time. It's a cross-platform issue and it seems very many people have it. I presume it will be fixed during an upcoming patch. Hopefully.