Here you can get a government issued ID quite simply. They usually require one of the following: source documents like birth certificate, baptismal certificate, social insurance card, or healthcard. Proof of residence can be as simple as the provision of a utility bill or other statement showing your name with current address. Surely you have at least one of these.

As for payment, if they won't take cash then get yourself a prepaid credit card. The best place to obtain this is your local post office.