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Start doing jobs in your spare time, build up your "portfolio", and then you can have more experience to put on your resume.
Any delusions though about this not taking a couple years should be expelled from your brain, having a non-programming degree and trying to break into a saturated job market with people who have been programming professionally is especially difficult. This isn't the .COM era anymore where we had a hard time finding talent, people are working for peanuts just to have a job near code.
To add to that, realize that there are thousands of programmers coming out of school right now with a degree in programming (Computer Science or Software Engineering) that can't get a job. These are highly qualified individuals who lack experience, its an employer market right now, meaning the favor is on the employer to get exactly what they want. The job market is still recovering and we employers can be very picky.
On top of that, if you are applying for a programming job and you mis-represent yourself on your resume to get your foot in the door (talking up your skills, experience, etc) this is usually where the interview immediately ends. It doesn't take long for a good recruiter to figure out how much bullshit you put on your resume.
It is not an employers' market in the whole country; there are developer shortages in the major Texas cities (and, from what I hear, also in East Coast cities). Since 2011 or so, employers have been outbidding each other to get experienced candidates to join them.
It might not be quite that good for entry level employees, and there might be parts of the nation where the demand is low, but it's far from an employer's market right now.
Also, on another note, I never found any rent-a-code sites to be worth the time it takes to read the postings. Trying to get experience any way you can is generally a good idea, but those rent-a-code sites are among the worst ways of going about it.
Often the problem in job searching with little experience is "over-reaching". There are entry level jobs out there but what you want is a non-entry level job without the background to support it. You would really have to ace an interview to make that happen. The truth? If you Ace an interview, background is not an issue otherwise you would have never been interviewed in the first place.
The problem is that in programming this support experience won't be counted. If I start as fresher, it wouldn't be enough to pay off my bills and loan.
Seriously, after 2 years of support you are making that much more than entry level development? Having been there, highly unlikely. Also, why should your support years count towards development experience. If I took a support guy that has been here 10 years, he would be entry level in development.
support -> performance testing -> automation/simulation development -> development
Of course people rub thier eyes all the time with their (dirty) hands, which may be more dangerous since mouth is actually a pretty inhospitable place--it is the start of the digestive process (salivary glands begin the digestion of carbohydrates by secreting salivary amylase, which begins the breakdown of carbs and sugar). The skin of the hands is a lot more hospitable to bacteria and such, not to mention the chemicals that can get on the hands.