I would defer to people with more experience with the ins and outs of hiring in mainstream IT to comment on that, but I have one observation:
Whatever you've done that is unrelated to software development can be spun as a positive, on a resume and in interviews. My personal experience is that having a B.A. in English has been a very positive thing on my resume, primarily because engineering attracts so many people who hate writing for human readers, and have the poor writing skills to back it up.
Your success in finding a software job are really going to be determined more by your ability to sell yourself as a problem-solver whose general intellectual abilities can make up for your lack of experience and education.
The other thing I'd say is that the number of jobs for pure C++ programmers is diminishing, and it's quite valuable to have some training and experience in the area of web development. The software industry as a whole seems to be moving towards a lot more web-based client-server programming, which means Java, JavaScript, Flash, SQL, and whatever the current flavor of the month is for web development -- Ruby on Rails, C#, etc.
And love it or hate it, learning to use the Microsoft web tools can get you a lot of jobs. Personally I think it's a lot like joining the Church of Scientology -- a whole lot of hermetic jargon, a whole lot of pointless BS -- but some companies are in bed with MSFT to the bitter end, and they love to see those certifications on resumes.