35 isn't old in the slightest. In fact, it's a very ripe age to get started as a Product Manager. Even if you were 90, there'd be nothing stopping you (other than your own limiting beliefs and maybe other people's perceptions of you) from being successful in the role. It's not like PMs do manual labor :)
Personally, as a developer-turned-PM-turned-Product Lead, I can ascertain that a lot of the advice on this thread is largely sound. I will also add that when you first start out as a PM, you will make a lot of mistakes, especially if you come from an engineering background (like me).
By the way, I'll be teaching a 10-week course on product management with Stanford Continuing Studies starting next month (April 2018).
https://continuingstudies.stanford.edu/courses/professional-...
It's fully online and much less expensive than a certification program. The goal is to teach you the ins and outs of product management and really prepare people for the role. Not kidding, I've spent hundreds of hours and a lifetime of learning into creating this course....it's the best course on product management out there, and the one I wish I had available to me when I graduated 15 years ago.
Here's a preliminary Syllabus:
https://continuingstudies.stanford.edu/courses/professional-...
Classes start the week of April 2nd, registration opens March 5th, and the class is limited to 45 students. Even if I wasn't posting this, I am told there's a high likelihood it'll fill.