Ate steak with the layer of fat kind of undercooked, is it dangerous? I bought a nice steak from a very good butcher yesterday. It was marinated in garlic and oil.

Tonight, I cooked it for about three minutes on each side (probably more). 

The layer of fat on the steak, when I cut into it, was still kinda pink. It looked "raw". I ate it (or basically, sucked the juices out because I couldn't eat the fat as it wasn't breaking down [it never does really]), and it tasted great, but I'm a bit worried that it was dangerous.

Like I said, I fried it for at least 3 minutes on each side (the two sides). The rest of the steak was fine -- probably about medium to well-done, just the layer of fat on one end which was attached to the meat was kind of pink and fleshy. I think it's the bit that connects the fat to the rest of meat that was pink, and maybe some of the meat nearby it as well.

Will I get ill?

I saw the other thread on eating undercooked steak but I think my thread is different.
It is not (immediately) hazardous to your health.  I say immediately because I would not recommend eating fat or gristle en masse.

I used to marinate my steak every time I prepared it.  I have gotten away from this habit.  Marinating breaks down the integrity of steak.  This is desired if you are cooking a less tender cut.  I eat steak less frequently now, and for that reason, I choose to get ribeye or strip.  If you decide to go this route, using dry rubs in concert with a good sear, or grilling, will offer you a very tasty meal.  Also, you will be able to gauge what fat and gristle really are - tasteless with a sickly texture.

As far as why eating steak like you mentioned isn't hazardous, given your description, it was cooked at least medium.  There is a large segment of the population which chooses to eat rare steak.  This type is deep red and cold in the center.  While it's not for me, I've never heard a Surgeon General warning that says rare steak should not be eaten.