If I apply for a loan what are the chances I'll be approved?

I have had some credit issues in the past. I'm currently 21. When I was 18 I was kicked out for getting my nose pierced, and had to live with a friend. I had a job that paid me 7.40/hr and was going to college 2 days a week. I moved out of my friends house into a mobile home with some roommates, so I had to drop college to pay rent. I had to take out an $800 loan to drop a cl and completely forgot about it until right now...I have not been contacted in anyway about this loan and it's been 3 years. Needless to say I forgot about it. I had signed up for a Maurices card and was doing fine with that until my hours got cut to approximately 20/week. I had rent, car insurance and a phone bill plus gas and food expenses. So the Maurice's payment wasn't the first thing on my mind. I paid it off a while ago, around 2 years, and I though my name was free and clear...until I remembered that stupid loan that the college clearly doesn't care too much about. Anyhow, taxes are coming up and I'm claiming head of household along with dependents so my return should be decent. I was going to apply for an auto loan to get a used 09 Cobalt from a dealer, but it's a little under $10,000 hence my need for a loan. Am I going to be denied because of this $800 forgotten college loan, and If I pay it off when my taxes come in will I be able to be approved then? Also am I going to need full coverage on this car with an auto loan or can I just get PLPD on it?