Help: Car won't start. Serious electrical issue or minor?

Hi all. I will describe the situation as it happened and let you help me figure out what is going on.

I was out of town for about a week. I drive a 2008 Prius with about 35k miles and no previous issues. I get back tonight and go to open the door with keyless entry. Nothing, doors wont open. I hadn't replaced the batteries in the remote since I bought it, so I figured it was just that. I use the key to manually open the doors. I then go to start the car. Nothing. No lights, no noises, literally nothing happens. I figure, perhaps I left a light on while I was away and the 12V battery is drained. It is quite the rare thing, but it has happened a few times in the past. Usually I would catch it the next day and be ok, so maybe a light was on for a week and that did it.

So at this point I assume it's just a dead 12 V battery. I ask my friend to give me a jump. We open the hood, connect up the jumper cables in this order : + Prius, + and - to his battery, then - to the Prius frame. Quite a few sparks fly, which seemed like more than what I was used to seeing, but it doesn't seem too outrageous. I try to start the car and nothing happens. My friend then tells me he accidentally hooked up the jumper cables backwards. (I know now this is bad, and may be the source of the problem but please hear the rest of the story to get a complete picture of what's going on).

So we swap them on his battery and try again. I put my foot on the break and push the power button. His car is still running in the background. The power button LED then turns green, and that is it. No noise or anything else. I then (while keeping my foot on the break still), push the power button again. This time the power button LED turns orange, the parking break P LED turns on green and the check engine light on the dash turns on. Also I think the car also makes the normal humming sound we are used to hearing when it turns on. No other lights are on at this point. The main display doesn't come on, nor does the interior lights work, or anything else for that matter. The only thing functioning from inside are those 3 lights. I turn the car off and we just figure it needs more time to charge. So we give it a few more minutes of charging and still the same thing. We notice a strange thing. We hear a clicking sound coming from the fuse box area of the car. Every 5 seconds or so, it sounds like a relay clicks, and then clicks off after 2 seconds or so, and this continues on. My friends engine sounds as if during those two seconds like it is sending current to my car (lower engine rpm). So it sounds as if the relay sends current somewhere for a few seconds and then no current goes to my car, 5 seconds later it sends current to my car then 2 seconds later no current, etc. This goes on continuously and we are not sure why.

We figure maybe a fuse is blown. My friend checks the fuses we think to check but can't seems to find anything wrong there. We then think maybe the power needs to be disconnected to the electronics to allow capacitors and what not to discharge. So we disconnect the lug from the jumping terminal (the one we connected the + jumper cable under the hood) for about 10 minutes. We reconnect the lug back 10 minutes later and try again. Same things with the lights and buttons pushing as before. The only difference this time is you can get these lights to turn on without having the jumper cables connected (as if some of the battery was charged).

Next we figure, maybe we just need to hook directly to the 12V battery in the "trunk". So we connect to that. Now, instead of having the relay tripping every few seconds we don't hear the relay tripping at all. And the engine rmps are operating constantly as if it is consistently drawing current (constantly lower rmp sounds). So that is different this time than when we connected to the post under the hood. So we continue running the car at high rmps for a few minutes and try again. Still the exact same thing with the lights.

Also during these tests the break pedal seems to put pressure on itself when you hit the power button a second time and the lights turn on. (This is just a detail to include, I'm not sure if there is anything useful to gain from knowing this).

Anyway, I know the problem is most likely that everything was fine until my friend accidentally hooked his end of the jumper cables to his battery. But in the event that there is something else I should check, that would be greatly appreciate before I have it towed to the Toyota dealership here.

Thanks in advance for any help.

P.S. and FYI, I have a bachelors and masters in electrical engineering so feel free to be as technical as you feel necessary with the electrical stuff. As far as car specific technology goes I am not quite as proficient with and would like the standard car dummy terms and explanation .