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This sounds a lot like a throttle module problem. There is one thing you can try and that's to disconnect the negative terminal on the battery, then touch the negative cable to the positive terminal for about 30 seconds to reset the system. Try to start and run it after that. This sounds like something has lost communication for long enough to get it out of phase with the engine computer. Typically this is sign of a throttle module problem cropping up. Did you get an "ETS" light on the dash when this happened?
One of them should be a yellow one. That's the main relay. Check the base of the relay and see if any of the terminals are discolored. If they are, it's probably not working correctly.
Having someone change a battery at Autozone is like playing Russian roulette. If they hooked the terminals up backwards, that could easily cause the problem your having. Hooking up the terminals backwards even for a second or two plays heck with the software in any of the modules. Hope that's not the case.
Hate to say it, but you may have to have it towed to someone that can hook it up to a diagnostic computer and read faults. My recommendation would be a dealer as they are the only ones that can download software if it needs it. Also, if it's a throttle module problem, they are covered under an extended warranty for 10 years or 200,000 miles. Having that done somewhere else can cost close to a grand. If the dealer finds a problem with the throttle (which is what I'm suspecting), they'll replace it under warranty. BIG savings if that's the issue. The symptoms you're describing are typical of a throttle module failing, losing it's power supply or losing the software. Best to rule the power end of the equation out before having to tow the car.