You need not be in the vehicle at the time you are arrested for DUI.
It is rather interesting, however, that you don't believe you were in the car at the time your car swiped a parked car and that you never realized it happened. That will be a rather interesting argument to present to your attorney. Please hire counsel.
First, hire a lawyer! You do not have to be "caught" behind the wheel. The state can use circumstantial evidence to put you behind the wheel. Obviously you have an interesting story and you should explain it to a qualified attorney that knows the ins and outs of DUI law in your area.
If you were arrested you will likely be charged.
Your situation sounds like you have some considerable defensive issues that could make the case against you difficult for them to prove.
You need to get a lawyer.
Yes, you may be charged with DUI even if the arresting officer did not see you drive the vehicle. In Illinois, you may be charged with DUI of alcohol or drugs if you are in actual physical control of any vehicle under the influence. Did you give your keys to someone else? If not, you could be deemed to be in control of the vehicle while drinking. You should retain a qualified DUI lawyer in your area in Illinois to assist you in presenting your best defense. DUI cases are complex and turn on the independent facts of each DUI arrest.
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As stated by others, you don't have to be caught behind the wheel to be charged with DUI. There is probably enough evidence to tie you to the vehicle though. Maybe you beat the DUI if they cannot show you were under the influence at the time of the accident, but you could lose on leaving the scene of an accident and depending on the amount of damage have your license suspended and/or the Class A misdemeanor for failing to give notice upon hitting an unattended vehicle. Get a lawyer right away to minimize your exposure.
This answer is provided for informational purposes only and does not create an attorney-client relationship. Follow-up with a licensed attorney who regularly practices in this field is strongly recommended.