I agree with 3minus1, you should definitely know why you were fired. New managers seldom want to fire someone without cause and typically have HR hoops they need to jump through to do it. I have never let anyone go that wasn't first given verbal warnings, daily check-ins and at least one formal write up that outlined the job requirements and what was needed to set things right. Hiring good people is hard and it is better to get the most out of the people you have before giving up on them. Of course this isn't always the case but some of your managers or HR should have shared something with you.

How many jobs are you applying to each week? I would think 1 or 2 each week would be a minimum.

Do you have a portfolio? Some code you can point to online, any open source projects you work on?

How many interviews do you average each month? If you are applying to tons of jobs and not getting any interviews, this is a reflection that your resumes might need work. Resumes, plural, in that you should probably have several depending on what type of job you are applying for and what skills you need to emphasize. Maybe you need to drop some jobs off of it or rework it to look more like you have been courting contract or short term work and now you are ready to "settle down". Have you filled gaps with additional university courses? Pursued a Masters degree? Certifications? Traveled the world? Volunteer work? Freelance/Started your own business?

If you are getting interviews, but not job offers then this indicates it might be a problem with your interview style. You mentioned depression, could this play a factor? Hopefully you don't bring up medical conditions during interviews. It could be some of the things you say during the interview process, not saying enough, questions you ask, what you wear... any number of things. I almost didn't hire someone because of the socks they wore but my team defended their choice of footwear and we hired them in the end... though the guy in the Christmas sweater wasn't as lucky :)

Have you tried teaming up with a recruiter? A good one would help you with your resumes and interviewing skills. Are you keeping in touch with former classmates, colleagues and managers? Not just email, set up lunch dates with them to stay in touch. Set up a small lunch reunion from a company you worked at where several people were all laid off or have since quit. They may have leads from time to time. Looking for a job can be a full time job in itself!

Good luck!