Since you are only seeking a $3,500 loan (plus another $1,000 or so for taxes, doc, license depending on your part of the country), you probably are in a better position than you think. Depending on the age of the car, I might start out by talking to a credit union. They are much more transparent to deal with than a dealership. The rates are often clearly explained at the credit union's website, and while they may be a bit higher for a low credit rating, these folks are usually very easy to talk with. So it's a "safe" starting point.
Also, you say the asking price is $11,000. I assume you haven't negotiated yet. You may actually be seeking a smaller loan if you get the price down to say $10,500.
With all respect, if you have a low credit rating, I assume you are not a homeowner. But on the offchance that you have a home equity line, this could be a great option for you. The interest is deductible and depending on the specific equity line, you may have some flexibility in say getting a fixed rate for a fixed time. And, pardon me if you have recently lost a home to foreclosure and are suffering a credit score drop. So many folks are in this position.
Hope this gives you some direction. Good luck.