Ringo, having been involved in computers/technology/engineering for most of my life, and now being a few years away from retirement, I would like to share just a few thoughts.
It is quite possible to enter a programming career with no formal training. However, most managers are unaware of that, and one of the first questions you will get (if you even get to an interview) is going to be about your training. Just imagine how you are going to word your resume about being self-taught (without actually lying about it). Now imagine defending that at a formal interview. There are also a lot of unemployed programmers out there right now. With the end of the cold war, and many companies deciding to go with a "world economy," there will continue to be unemployed programmers for many years. There is something to be said about an unhappy job that has a good chance of being there for many years to come. I know a number of programmers who would be happy to be complaining about their boring job (if they only had one). Also, most programming jobs are actually temporary jobs. You would be there to do a project, and then get laid off when the project is done. You would work for a lot of different companies, and that doesn't look very good on a resume, either.
I think that the advice of pursuing an advanced degree which would combine your accounting skills with some computer skills would be a good way of getting your feet wet, without completely changing your career options. As a word of caution, though: As you get older, an advanced degree is not always seen as advantageous by the hiring managers, because it means they will have to pay you more. Most managers would rather hire staff that are cheap, rather than competent. You might consider educational programs where you get a certificate of accomplishment, rather than an actual degree. With the increase in age before you can draw Social Security, you will want to remain employable as long as possible. I know it seems like an infinite amount of time before you get to that point, but you will be laying the foundation today for what will happen in the next several decades.
However, after saying that, if you really desire an advanced degree you should probably go ahead and get it. Some of the hybrid degrees (accounting/programming) have their own niches in industry. As long as you have your primary accounting degree to fall back on for bread-and-butter jobs, you have a lot of freedom for pursuing something else, either as a hobby or a second career.