How do I sign up for Medicare?

I will be 65 years old next month(January). I do not have enough quarters to receive Social Security, However, I have enough quarters to receive medicare, in fact, I am retired (State) and work part-time and medicare payments are being taken out of the meager earnings that I receive.

When I ask the local ssa officials in my hometown about applying for medicare, I was told since I did not have enough quarters for Social Security I could not collect medicare.

Something about this does not sound accurate.
I do not have money to hire a lawyer, What's my next move?

P.S. My husband was turned down for the same reason, although his yearly statement says he has enough credit for medicare. He is 72 years old and gravely ill. Please advise.