Short answer is yes you can be charged. It does not matter whether it is moving or not or whether it is operable.
This is not legal advice. This is merely a recommendation on how to get what you need from the Court.
In answer to your question, "Can you be charged with a DUI...?" The police always have the discretion to charge you with a DUI. The real question is, "Can you be convicted of the DUI under those circumstances?" This type of case is called an actual physical control case. This type of case is the case where you aren't actually driving but you are charged because you COULD exercise control over the car. I have won two separate actual physical control cases because the car was inoperable. In one jury trial in Kendall County, my client was sitting in the driver's seat intoxicated with the keys in the ignition when the officer arrived, but the car had stopped running because it was out of gas. Her boyfriend was present and had admitted to driving the car to that spot. The result = not guilty because she could not actually exercise control over that vehicle. I won another bench trial in Kane County where my client's car was inoperable and in his driveway. During a party he sat inside the car to talk on a cell phone. The police came to the scene due to noise from the party, made some assumptions, such as that the keys in his pocket fit that particular car (never checked to see if they did), asked my client to perform field sobriety tests and arrested him for DUI. Although he was actually intoxicated, the Court found him not guilty because the state had to prove he could have driven that vehicle and did not present any evidence that he could have if he wanted to. In my opinion, any of the fact patterns in which you describe certainly deserve trial consideration.
The state need only prove you were in actual physical control of a motor vehicle while under the influence. Thus, the out of gas part does not help you much. However, it does open the door to other defenses depending upon other facts which are are not mentioned here. Also, merely pushing a vehicle is not necessarily actual physical control. You should consult at least two experienced criminal defense/DUI attorneys and then hire one. Most of us provide free consultations. www.galivanlaw.net
In Tennessee you could be charged if the car was out of gas because putting gas in it would make it operable and you are assumed to had driven the vehicle to the location you ran out of gas.If its a mechanical situation, then your defense would be better because the car could not operate due to the failure of the engine and nothing you could do in a moment to fix it.
. I don't know if this is the law in Illinois.