Hate to say it, but I'm afraid your chances are slim to none unless you have some crazy connections (i.e. you are the son/daughter of a 20M/yr client). Most firms will only consider the top 5% or so at a tier 4 school. It may be snobbish and unfair, but that's generally the cutoff. Usually that cutoff is only deviated from under extraordinary circumstances. Additionally, most firms do the vast majority of their hiring through OCI. Since you are asking the question, I'm assuming that boat has already sailed. My advice is to start networking aggressively (search around for old posts from Matthies on the subject).
Outside the top of your class at T3/T4 you're not getting a traditional big firm SA job, but of course it always holds that the only time you really have no chance is when you don't apply.Apart from your traditional big firm SA jobs, if you are looking for a paid position I would consider:medium / small firmsfellowships (such as various ABA ones)paid federal or state gov jobs (attorneys general, alphabet soup agency)paid research assistantGood luck ! I'm a former T3 student and almost had a paid 1L gig through an ABA fellowship, I don't think school name matters much with those.
Just a couple of examples:Steiger Fellowship in Antitrust / Consumer Protection Lawhttp://www.abanet.org/antitrust/at-law-student/at-js-project.shtmlPeggy Browning Fund (workers' rights, etc.)http://www.peggybrowningfund.org/
Biglaw is probably out of the question, but you can try for small firm gigs, government jobs or public interest. Networking is key, so do take the time to attend every little wine & cheese hour or talk your school hosts. I certainly didn't feel prepared to do it right after graduating from law school, but you could go solo.