Absolutely! I'm 29, college drop out. Always liked computers, but never really programmed. Didn't do much for years, then just dove into php about two years ago. A year and a half ago, I got my first tech job making web site updates. That's when I really started learning a lot. After a year, the guy above me quit and now I'm the department head (though small department, lol). It feels like once I got my foot in the door, everything fell into place-- so that is the hardest part for sure.
Now I am starting to venture into other languages like Ruby and C in my spare time and I am excited to see where I'll go next. I know you are older, but its a similar story. Really, as long as you are into it, you will catch up in no time. And once you do it for a job, you will never look back. If you need a boost, take some online courses, go to meetups, sign up for a web development bootcamp. Meet other people who do web, you will find that a lot of people doing it now didn't start life as a programmer either.
Now I am starting to venture into other languages like Ruby and C in my spare time and I am excited to see where I'll go next. I know you are older, but its a similar story. Really, as long as you are into it, you will catch up in no time. And once you do it for a job, you will never look back. If you need a boost, take some online courses, go to meetups, sign up for a web development bootcamp. Meet other people who do web, you will find that a lot of people doing it now didn't start life as a programmer either.