Hello, I’m back! 
I’m still having the same problem and wasn’t able to do anything about it until now because of finances. I’d like to reopen the topic and see what advice I can get again for this situation, and get it taken care of. Should I start a new thread? Or continue to use this one?
Thank you, for this service. Much appreciated!
Respectfully,
Guy
no need for a new thread, this one works just fine. 
Did you ever check your battery, alternator, and battery cables? Start there- just to rule them out.
Someone up above mentioned an electrical fault, but I am really wondering if this isn’t a slipping belt issue. RockAuto shows a mechanical, belt driver p/s pump for a 2007 RAV4, adn a slipping or stopped belt would explain a lot of what you have going on- except, I would expect it to break soon after not running properly.
Check the batt, alt, and batt cables, then check your serpentine belt condition. If you can, take the belt off and spin all the pulleys. They should all spin relatively freely, expect for the harmonic balancer- big one at the bottom.
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My first guess a failing ignition switch, Do you have a lot of keys on your key chain?
So, I just went out for a ride and came back, and when I Shut off my car there’s a weird sound, and I’m almost positive it’s my alternator. So that needs to be fixed but I’m not sold I’m not being the key issue. Will have that taken care of and then go from here. There’s a high whiny pitch noise when I accelerate and I just read someplace but that’s an indication as well as that it is the alternator. Once again I’m not sure why that has anything to do with the power steering going out but we’ll see. Looking for someone to recommend Dependable alternator since this will be the second one that I put in. I’ll be in touch thank you very much.
Cheers,
Guy
the high pitched sound could be your belt slipping. This may or may not be the alternator. there are several pulley running this belt, any one of them could be giving you an issue- which could in turn cause the alternator to flutter.
It is common for those alternators to whine when they are failing.
The power steering control module will shut off the power steering when the battery voltage gets too low.
Ahhh Ha!! Now its all making sense. Thank you, Nevada, for that heads up!! It’s not fixed yet but I think we’re on the road to Toyota RAV4 recovery! 
The power steering unit electric and is located under the dash;
I’m having the same problem with a 2006 Rav4 Limited (4-cyl).
New battery Sept, 2019. New alternator November, 2019. Under normal circumstances, batt light comes on at low RPM. Raising RPM to about 1000 turns the light off. The problem has occurred three times in the same manner as described - engine stays running, all dash lights come on. However, the last time it happened, the car was towed home and the battery was depleted to the point the engine wouldn’t turn over. The battery was subsequently charged, and the car has since been used for one 20 mile round trip.
My problem did, in fact, turn out to be a bad alternator. Even though it was 3 months old, it had failed. Since it was replaced, the problem has not reoccurred.
There is a rather easy way to keep an eye on your alternator. Pick up a voltmeter that plugs into the lighter socket (there are plenty on Amazon). It should read about 12.5 V before you start the engine, and somewhere between 13.5 to 14.2 V after you start it. If it does not increase after starting the engine, it is very likely the alternator is bad.