You are definitely not too old! I was 33 when I finally decided to join the game industry. I applied for the one job I wanted, got it, and have been at it for over 7 years now.
However, I had an ace up my sleeve. To avoid the dreaded Catch-22 of not having game development experience before getting game development experience, I designed, programmed and sold my own game. If you can do something similar, you will develop needed skills and show that you have the drive to be a game programmer. Any decent programming manager will respect that.
Let me ask you this important question, WHY do you want to join the game industry?
I'm not being snarky, it's a rough business. I have never played so few video games in my life since joining the game industry. The pay is far less than what you can make in a non-game industry job. For example, by best friend who is my age, same brain power, same experience, heck - we even worked for many of the same companies, now makes 150k a year not including bonuses or stock. I make far less than that.
I'm not trying to talk you out of it, I just think you should know that once you start making games, you will be playing far fewer of them, and not getting paid as much, or at least not at first.
That said, I love my job and the company I work for. The work is exciting and every year or two you have a new project to work on.