What are the key a and b wires on my boss stereo for can they be bypassed

Question edited for clarity.

It's a guess, but..... Because it only works with the door open, I am thinking there are broken wires or chaffing where the wires go from the door to the door jamb. 12 volt power, grounds and speaker wires don't mix and could have easily blown the circuitry in the old one.

its like that for good reasons

Check at your local car stereo installation store, or on eBay. You should easily be able to find an aftermarket harness for your car that will easily attach to the harness for your Boss stereo.

Try to make sure the red wire is going to a switched power source. That is, a source that is off when the key is off.

Yes, you can bypass parking break feature by connecting the corresponding wire of BV8962 to ground, also you could add a 3 pin toggle switch to get a normal and bypass mode switch, this can be wired of this way, the common pin of toggle switch to your video unit, at the other pin, it could be connected the parking break wire (normal mode) and the remaining one to ground (bypass mode).

Yes, you wire the head unit wrong, there is ground, batt12v constant(usually yellow) Constant because you radio memory, Accessory wire when the key is on(that way your radio turns on and off with the keys, and last but not least you ILLUMINATION WIRE witch when you turn your headlights gives you curren 12v...
ground
Batt 12v
Accessory (on with the key on number 2 position)12v
ILLUMINATION. 12v when lights are turn on

Connect the pink/black wire to ground to bypass.

it could be that either of the two power wires is loose

Earth the cable to the back of the stereo casing using a screw or insulation tape, it fools the stereo into thinking the e-brake is on and allows you to watch DVDs on the move. Just use with caution, i did the same for my old one and its surprising how much of a distracion it can be whilst driving

Boss Audio is the easiest in-dash DVD on the market to bypass; all you do is ground the ebrake wire. I recently installed 12 Boss Audio in-dash BV-7300's and did this to all of the decks problem solved. By the way I did this because they were in the back of limousines where the driver couldn't ever even see one of them while he was driving. I don't think there will be a problem, try it.