When I got arrested for OWI but my car was not running and my keys were not in the ignition, plus my rights were not read, what is my legal recourse?

You can be arrested for drunk driving even if you were not driving at the time.  The fact is that the police do not have to actually observe you behind the wheel of a moving car.  All that is needed is evidence of driving. You admitted that it was your car and could be legally sufficient to demonstrate that you exerted control over the vehicle. Additionally, I don't know what, if anything, you told the officer at the scene.  That coupled with a failed sobriety/breathalyzer test (you did not indicate) test would further legally establish that you not only exerted control over your car but did so at a time when you were legally intoxicated.

This, however, doesn't mean that you don't have legal ground on which to fight this charge.  There are defenses that can be enlisted in your case which could result in a reduced charge or outright dismissal.  Your best bet is to now consult with a DUI attorney in the area where all of this occurred.  In addition to any legal arguments that can be made on your behalf, they will also have contacts within the local court system that they can utilize to your advantage.  A DUI triggers both civil and criminal cases.  You really should have legal representation.

As for being read your rights, even though you were arrested, so long a you were not questioned after the arrest, then there is no leagal requirment that your rights be read to you.  And being asked your name, address, and the like does not count as "questioning" for purposes of the Miranda warning.