There are some good advice to you question, but I would like to point out two.
This:
One shouldn't learn how to use a programming language, but rather the fundamentals of programming. Once you know the fundamentals, switching from one language to another will be easier.
And this:
Do you want to stop being a SysAdmin? DevOps is starting to become more common where you develop the systems and administer them as well. This means that you won't be throwing your SysAdmin experience away but building on it to reach a more advanced position.
Here's my story/advice:
You never too old to learn anything, or be competitive in a market where companies prefer junior Devops. Being certificated means Jack sh*t if you do not have the experience.
I'm pushing 51. My vocation was an electronics engineer. 10 years ago I had this brilliant idea for a project but I needed a website and web services for that. So I started studying PHP and MySQL (and then later JS, HTML, CSS, etc.).
8 years ago, I got fed up with the electronics and went into web development, specifically back end development, full time and Drupal CMS with its API.
Today I am senior developer and team lead for a large project.
So, here is my advice, and why I quoted the above two.
Get yourself a little project for yourself. You want to learn C(#, ++)? Start thinking out the box. Get an Arduino. Create a special project for yourself at home that is fun. You would be surprised how much you learn when you do something for yourself.
Make the Arduino talk to a server > webpage. Now you might be learning a bit more about PHP, Java or Python, etc. You would be surprised on the similarities (thus quote no.1).
Or, since you in IT, You might know Linux. Get a RaspberryPi. Runs on Linux, but you can do your own custom programming (I'm not sure which languages, but I think Python is one of them). (thus quote no. 2).
Things I've learned:
1. Don't try and learn everything for a specific language. Get the basics. You want a specific function? Then search Google and study it.
2. Be prepared to change your mind set of what you know now, and accept new challenges. Case in point from me being an engineer. The programming I did during that time was very logic based (if this then that, type of thing). I had a tough time mastering
OOP, but I did. (Another reason for quote no. 1, OOP is used in many languages).
3. Get experience, a lot, and a lot of different scenarios. As I said before, certificates does not count if you don't have experience (In my current job, I also review CV's and sit in with interviews. 90% I would recommend a person with experience over a certificate.)
4. Have fun. As people said here, if it does not give you pleasure, don't bother.
5. Oh, also what others said, it can be a very lonely job. But then it could be about self satisfaction nailing that problem.