2003 Prius won't come out of Park

Okay you experts, I have a problem with my 2003 Prius (having 220k miles) not being able to shift out of Park. I've scanned and read all the relevant posts I could find on the matter, and came to the conclusion last night that it would either be an easy brake switch fix or possibly a much bigger stator coil replacement--the former seemed to be more likely because I can hear and feel the transmission making changes as I move the shift lever between gears (P/R/N/D/B), but in every case I could rock the vehicle back and forth a couple inches and was able to confirm it was still in Park.
Before anyone thinks I might be new to this--No, the Parking Brake was not engaged, and Yes I know that I have to press the brake to move the gear shift. In fact, my troubleshooting this morning prior to calling AAA to have it towed to my personal garage was to remove the lower dash cover, disconnect the brake light switch, and jumper the connector (turned out to be a purple wire to the black/yellow striped wire as opposed to black to blue that another post had provided--which was close enough for me and enabled me to actually move the gear shifter without pushing on the brake.) No success however--it remained in Park.
So my only other conclusion that I have been able to muster from all you who are more knowledgeable on Prius matters is that it could be my main stator coil has a burned wire. However, none of the symptoms of that failure seem to match up with mine--I still can start and rev (slowly) the ICE, and only after I had toyed with this thing yesterday afternoon for awhile did the red triangle come on (and I'm not even sure how much time my son and his friends had spent trying to get it to run before I got there)--this is now my son's first car, having just got his license 2 weeks ago, so there could have been another factor that he's not fessing up about--but it was not in any accident and was courteously parked in front of his friend's house and the friend's dad said he had tried to give a go also before I was able to get there.
Sorry to belabor my question with all the above, but does anyone have a thought why I cannot get the transmission to move from Park, even though I can hear (and even slightly feel) it 'shifting' in the transmission?
By the way, I have personally rebuilt this traction battery twice in past years (most recent was less than a year ago), and I converted from the wimpy Toyota Aux battery to a regular car battery several years and many miles ago.

 

Haven't verified, but I've had many problems with the aux battery over the years and never seen this symptom. I can hook up some additional juice but I am not confident that will do any good. Gonna be a few days though as I am not close to the car right now or able to troubleshoot until Friday

 

And thank you for your timely reply!!

 

Thanks Chapman! So do you think it really may be more of a transmission problem after all? I really don't understand the CVT, even though I am an engineer and have seen the diagram a few years ago. Does anyone believe my situation is consistent with a stator coil failure?

 

Okay thanks again Chapman. That makes me feel a little better although possibly without basis. So I guess I will be looking into the transmission a little closer.

 

Okay, ran out of time in early July before a family vacay. Back to it now and I think I have confirmed that the cable and interior linkage is all good, which is bad because I can't figure out how or where the cable enters the tranny (must be under the inverter assy). I can hear the shifter doing something inside the tranny but it's definitely not coming out of park in any gear shift position. So do I need to remove the inverter I guess? I've removed and rebuilt many batteries now, but never had to do anything with the inverter

 

Thanks again Chap. Sounds like I probably need to get a copy of the manual you are referring - can you point me to where I can get one?

 

I didn't really think the key trick would fix it, but for $29 I figured I would give it a try. Unfortunately, no, it did not solve the problem. I have acquired a 90 day access to the Haynes manual and will be going down and in to see where the cable/linkage is disconnected or broken. More to come when I get in there. My son is adamant that he just parked it at his friend's house that day and when he was trying to leave he couldn't get it out of park--very odd failure indeed.