For me, the fact that the original used "bring/brought" makes it very unlikely that it's being said on any day other than the actual birthday. If I found out I had missed someone's birthday by a day/week/month, I might say "If I'd known it was your birthday, I'd have bought you a present". I note that Tarheel's response in post #9 specifically refers to buying a present.
I would use "If I'd known it was your birthday, I'd have brought you a present" only if I was in the company of the person in question, it was their birthday that day, and there was no opportunity to get them anything. The most relevant of those three conditions is that I'm actually with the person when I find out it's their birthday. I would have brought the present to them. I could be at work with them, or at college, or at a tennis lesson - but we would have to be together.
On the topic of "buy", though, I tend to avoid using that verb when talking to someone about a present for them. I try not to involve any mention of money. I'd use "What can I get you for your birthday?" or "I can't decide what to get you for Christmas".