Can't buy Great People

Multiple poliy trees grant you the power to buy Great People with religion come industrial era. I have completed tradition which gives this ability for great engineers, I'm no 3 techs deep into my industrial era, and I still do not have this ability.
I did not manage to found even a pantheon at the beginning of the game and my only city (Venice) has 5 religions but no majority one. My religion tab says I'm not eligible to buy any great people with religion.

Am I missing something, or is the game broken?

I think you need to have a state religion and it must be present in the city you are trying to rush buy great people in.

You can only buy a GP in a city where a religion is dominant (I doesn't need to be your religion).

Edit: Also (of course) you can't have a civilian in the city (same as when you buy a military unit, when you can't have a military unit in the city).

Thanks. Got to redirect all those trade routes according to a religion, then. Gonna miss rushing the Louvre, though, which is a darn shame. I really don't want Brazil to beat me to it and I'm going to waste 12 turns of production if I switch from Big Ben now =S

Never Mind.