You must include into income in the year of receipt, the fair market value of the vehicle. It will be classified as ordinary income reportable on the miscellaneous income line (line 21) of form 1040.
You will likely receive a Form 1099-MISC from the contest sponsor showing the $16,500 as a prize received by you. If you intend to dispute that amount you need to round up proof of the FMV you intend to claim as income. You cannot use the amount you sold the car for (unless actual FMV is euqal to or less then $13,000) since it is considered to be "used" at that point (even if you never drove it off the car lot). What you should do is get on the internet and find out what you could buy the exact same car for (i.e. same options, etc.). Retain the documentation once you have proof that the FMV is less then $16,500. You cannot report less then what you actually received. When you file your return attach an explanation of why you used the amount you did as well as a copy of your documentation.
With respect to the sale of the car you effectively have at best a break even transaction. Your cost basis is the income you report. So if you end up reporting $16,500 as income, you have a loss on the sale of the vehicle of $3,500. Since the vehicle is a personal asset, the loss is non-deductible.
Save some of that $13,000 to pay the additional taxes you are going to owe. You may want to consider making an estimated payment by 9/15/05. See form 1040-ES at (http://www.irs.gov/pub/irs-pdf/f1040es.pdf) to make a Federal estimated payment. See form IL-1040-ES at (http://www.revenue.state.il.us/taxforms/incm2005/ind/il1040es.pdf) to make an IL estimated payment.
Because it is impossible for me to identify and consider ALL the relevant facts, this advice is not intended or written to be used for the purpose of avoiding penalties, and cannot be used for that purpose.