Reach your mid 30's as our OP is heading towards and very few people are going to be looking at 35 year olds who have done nothing but have just spent 2-4 years at University gaining a tick box, there are far younger people without such baggage who are likely to be much more hungry.
Yes, I'm pretty sure many professions are closed to me due to my age. Software development, for instance. Nobody is going to hire a 35 year old junior programmer. By the time you've got a portfolio under you belt you'd be retiring
But isn't it going to be like that for almost *all* professions? I can't think of many employers who wouldn't rather have a 23 year old starter than a 35 year old starter.
So it's not going to be easy. I imagine, like has been already said, I'll be facing a lot of rejections, and very little interest.