I am trying to buy a new car. However, I have a $3,500 subsidized student loan. I've had it for about a year and haven't made any payments on it. Will this affect me getting a car loan? Will it be wise to put some money down on the student loan before I apply for the car loan? Let's say $500.
Repayment of student loans is usually deferred until graduation.
Unless you are late or non-performing on a loan, it will make no difference to an auto loan.
To get a (normal) auto loan you will need to demonstrate a source of income or have the loan co-signed by someone who does have income.
As a general rule of thumb, banks care a lot more about your income than your "credit score".
$3,500 isn't usually enough to make a difference when calculating credit for a car loan. The other factors that you didn't mention are the important factors. How much money do you make? What is your credit score? Do you have balances on credit cards? The only way you can know is to look at your credit score and/or apply. I would generally recommend you buy a 3-4 year old car rather than a new car. With the lower purchase price you can pay it off quickly.
I like Nathan's answer some, but am horribly curious as to why you have not made payments on a $3500 student loan? If you are wealthy enough to afford a new car, this should be paid off next week. IMHO.
Above all else your financial goals should dictate if you buy a new car. What are they for you? If the goal is to build wealthy quickly then Nathan's advice may be to unfrugal for you.
If your goal is to impress people with the car you drive and accumulate very little real wealth then purchasing or leasing a car should be a top priority.
So to answer your question correctly one must understand your goals.
For 2016, the average car payment is $479 per month. If you invested that in a decent growth stock mutual fund in 40 years you'll have around 2.6 million. However, you do need something to drive now. If you can cut your car expense to $200 per month, and save the other $279 you will still end up with about 1.5 million in that same 40 years.
Personally I attempt to shoot for $200 ownership cost per car per month. Its a bit difficult as I drive a lot. Also I would not purchase a new car until my net worth exceeded 2 million. At that point my investments could mitigate the steep depreciation costs of owning a new car.