To be honest with you, DBA's no longer exist at many companies. Most modern databases are easy enough to use that all you need is developers. My current company has a single DBA for 7 development teams.
If you want to break into software dev the low hanging fruit is usually web development with something like PHP.
You're going to be competing with a ton of people that have degrees and experience so try not to get disappointed about your search. If you can't land a developer job straight away, I know many who have gotten into dev by starting as testers and building their knowledge laterally within the company.
It take the average candidate with experience and a degree maybe 4 interviews to get an offer, you will probably have to do at least triple that.