Sallie Mae Signature Loans, my chances of getting approved without cosigner?

I have no previous student loans, no bankrupts, I have a few credit cards that are current and are being paid on time. My only problem: I have some delinquencies that will be paid before applications. The delinquencies are not much, like 60, and 100 dollars each, but after going on for a few years have made my credit score go down. And I get denied certain things because of these. Will Sallie mae actually check and see if these things are paid, and see that I do pay my current cards on time. Or will the fact that i even had the delinquencies in the first place be my downfall even if they are paid. They said they go back like 7 years. But I have never had anything huge on my credit but small limit cards. No cars, no loans, so what are my chances..NO COSIGNER!! Also, already applied and got fafsa money, but it is not enough.