I have a similar story to you. I went to a no name school, with a liberal arts degree, a not so stellar GPA, no internships, etc.
I thought I wanted to go to law school school as well, get my paralegal certificate to see if I wanted to go to law school. Did really well and actually enjoyed it. Started studying for the LSATs and then the legal economy tanked and law school wasn't looking so great anymore.
Took me awhile to figure what I wanted to do.
I was able to get a job and was working though. There were times I hated it but it was better than nothing. In the mean time I scoured the internet to figure out what I wanted to do. I now have a job I enjoy at a Fortune 500 company.
This last bit is my suggestion. Stay employed, leverage your work experience, and then work on making connections. My guess is the emails you are sending you're not asking the right things, or your trying to connect with the wrong people. Look for lower level employees, email them expressing your interest in their company(and actually be interested) know things about their company and its culture, and request meetings to further discuss the company. DO NOT tell them you want a job or that you're looking for one. This will turn people off.
Find out where people network after work and get out and actually meet people. If you work in a big law firm you should be able to figure this out.
People will look at your prior record until you give them something else to look at too. If you can do it in your professional life, figure out an extracurricular activity you can get involved with and take ownership of. Network through these groups, take on projects, run events, do marketing or fundraising for them. Through this you'll add to your experiences and give yourself more to talk about when building connections and interviewing when asked behavior questions during an interview.
Fixing this situation will also have a lot to do with your personality and how you approach it. If you have a "woe is me" perspective, you'll have a harder time convincing people. Finding something positive to discuss and contribute will be key. Hating your job is one thing, but complaining about it isn't the best way to present it. Discuss what you've learned and how the experience has helped you grow and that it's not what you want to do, and that you're trying to learn what other opportunities are out there to help figure out the direction you want to go. You're essentially conveying the same message, but the tone comes across completely differently.
Not sure if this helps at all, but you asked for my .02 and thus I delivered.