I have a 2004 Honda Accord that I drive for business. Can I use the standard mileage rate for this old car?

The age of the vehicle does not determine whether you can claim the standard mileage rate. For 2018, you must be self-employed to claim deductions for business driving. And you must choose to use the standard mileage rate (and not deduct actual expenses) for the first year the vehicle is used for business. Also you can’t have 5 or more vehicles in your business. Otherwise you’re good to go (at 54.5 cents per mile in 2018).