Looking for first software engineering job

I am beginning a hunt for an entry level software development job, and I am not sure what actions I should take to improve my odds. Here is a list of current issues that I believe will stand in my way, followed by what I think I've got going for me:

Problems:
-Unimpressive work history: Worked for 1 year in college as a math tutor, and another year after college again as a part time math tutor from home during school year for an internet tutoring company.
-Never had a software development related job
-Only entry level skills, if that, which I am working towards improving (HTML & CSS, JavaScript, PHP, MySQL, C, Java)
-Only one decent reference (from an old instructor), due to poor networking and job history.
-I graduated in Spring of 2008. I don't know if this will seem like too long ago.
-Currently unemployed

Good points:
-Decent grades: Above 3.0 GPA from respectable state university, over 3.9 GPA from community college (got A.S. before B.S.)
-Confident that I have have at least a decent aptitude for software development/programming
-I'm sure I can learn whatever I need to for any job
-I'm willing to work for low pay for good experience (even free if the experience is good enough).
-I've been exposed to fundamental CS concepts, and understood them when presented (while earning my degrees).
-I'm actively working to learn new practical skills, and improve on the knowledge I have.

Other comments: In school, while I believe the classes I took were fairly rigorous (ABET accredited program, relatively selective university), I never took any software engineering classes (no agile development, design patterns, etc). These are on my long list of things to read up on.

So, in light of my situation:
-What are my odds of being able to find a software development related job?
-What can I do to improve these odds?
-Does any one have any suggestions about networking to get more valid references.

Take any job that pay for the rent and something as close to as software development. Helpdesk/Admin support type of work can be a good start and they generally willing to hire people without experience. You just have to have some work experience on your resume regardless what is it. It demonstrate that you are employable. An advanced degree usually help but it depends on your situation. Also, apply for internship if full time job is not within your reach.

Also, other than those famous schools like ivy, Stanford or technology specific school like georgia Tech, MIT, UIUC, no body really care so your work experience and what you can do is generally far more important in getting a job.

When you apply for a job, try to learn what the employer need and convince them how you can help.