As a programmer with no experience, knowledge of programming concepts is important. It's not so much the syntax as you can find many code examples and discern proper syntax. Java is [syntactically] a fairly simple language to learn. It also does a lot of memory management for you. You just need to grasp ahold of a few concepts.
(Note: At some point, I would learn C++. I'm very conflicted when it comes to helping someone choose their first language. C++ is not an easy language to learn as your first language. However, in an attempt to make development easier, other languages like Java hide some things from you that you'd be forced to learn with C++. The problem is, these things are beneficial to understand, even if you're programming in Java. The good news is Java is very syntactically similar to C++. So the best choice may be to spend some time learning Java and then try to jump into C++, simply to learn about how memory is really passed and managed.)
However, as I said earlier, mobile development is a different beast because mobile operating systems behave differently. The big difference is a mobile operating system's inclination to pro-actively kill processes and reclaim their resources. You have to code in a manner that assumes your app could be forcefully killed at any time. To effectively do this, you'll need to really understand the Android system, programming concepts, and Java. Mobile systems are not lenient like desktops. They're slow, low on resources and run out of power quick. This is also the reason why the Android Market is saturated with really bad applications.
(Note: While languages have caveats specific to them, many concepts cross languages. As a developer, you come to understand that syntax isn't particularly important. A good developer could write an application in a language they've never used before. The concepts are what are important.)
As far as your career change...
You'll need [at least] 1 of 2 things to get a programming job: 1) experience 2) a B.S. in a computer-related degree or above. At this point in the industry, having no experience, really the only way to break in is to get a Bachelor's degree. There are many developers with no degree, but the vast majority are older and have a decade or more of professional experience.
If you're looking to become a software developer, I would recommend a degree in Computer Science. Though understand that Computer Science is supposed to be less of a programming degree and more of understanding the theory behind computing (majority of your classes will be programming classes, though). At first, I didn't find much value in this, but as I grow as a developer, gain responsibility, accrue a greater understanding for systems, and learn to develop for different systems, I begin to appreciate it. It will also be very tough to manage a full-time job and get a degree in ComSci. Not that it's impossible, but it won't be easy. You'll be stressed.
Edit: Somewhere in this post I suggest that high intelligence is not a key factor in programming. Do not confuse that with Computer Science. There are classes you would take in Computer Science that do require a particular level of brainpower.
Typically, an IT degree will get you a job as a System Admin. Meaning you know your way around an Operating System and you have an understanding of networks, such that a business will hire you to keep their business and people running efficiently (you fix people's email when it stops working).
Some of this information may seem daunting, but I really don't consider software development to be for the particularly intelligent. I know very intelligent people who can't do it. It's more of a way of thinking. Some people think that way, some people don't. Of course a little common sense will go a long way, but that goes without saying. That will help with anything.
If I were you, I'd go to the bookstore, buy a book on Java development for beginners that reads like a textbook (examples, problems to solve, maybe some small projects, etc). Read through it, do all the problems, do all the examples, ask for help when you've tried and really don't understand something (pro tip: when asking for help on a programming forum, read the sticky post about posting guidelines and be sure to imply you've really tried to solve the problem on your own). Ultimately, books won't do you the justice that schooling will, but trying some on your own may elude you to your probability for success (I took my first programming class in high school. The teacher handed us our textbooks and told us to do exactly this and be done with a particular chapter by the end of the semester. In my case, the chapter was 5 and I happened to finish all 16. As I said earlier, it's a way of thinking; not about intelligence. I'm not a particularly intelligent person).
