My ground connector burnt. so I cut it off, now it does not initialize when the key is turned on, can I join all the wires together?

They probably cut wires under the dashboard that lead from the key mechanism that run down your steering shaft under the plastic cover if that is were the lock is mounted ? so have you had a good look under the dash to see if any wires are cut ? if you look under there and see wires that have been cut you can just join them back together by following the colour of each wire and joining them together , if the steering lock was smashed or damaged this might prevent it from starting as well .

all depends how short they were cut if there is a little length you can join wires together with connectors

Hi Ramiro, Im AL the owner of Big As Auto Repair.

Ramiro, any time a fuse is blowing or burning out, that means you have a dead short from power to ground. It could be wire's burnt together, could be a component shorted inside. I would start with the connector or splitter that you found that is burnt. Here's what you do. NOTE: Remove the negative battery cable before this next step. Then take one wire at a time and cut it on both sides of the connector and wire them together, each one of them. Be careful to wire the wires together that are coming straight through the connector. Solder and heat shrink the wiring OR at least tape it with electrical tape. Next, change the fuse with a good one and hook the battery back up. Next go put your hand on the wiring that you just worked on, if the wiring is not getting hot and the fuse is not blowing then you have fixed the problem. Hope this helps and please visit my auto-repair-website at: http://www.bigasautorepair.com/

If the kill switch has two wires: All the kill switch does is join both wires together. Find the two wires and ensure they are kept separated. If you want to kill the motor, join them together.
If it only has one wire: In this case, it usually bridges the coil to earth via the handlebar without blowing the fuse. An auto electrician may explain it better. Personally, I'd simply use the key to turn off or if no key, put a simple switch into the coil low tension lead. Also good anti-theft device as nobody knows it's there...

If you can see the ends of the cut wires then get some cable connectors from you local auto shop and join and crimp same coloured wires together.

It's called a headlight bulb connector, available at most any auto parts shop. They do melt, usually from use of high wattage headlight bulbs. You will have to cut and join in the new connector to your existing headlight wires.

Simply, no...but it's almost never simple is it?
In household wiring (AC) there is really no positive and negative, they are hot and neutral and ground.
Wire black to black, yes. But the green one is the ground and if you wire this one wrong you've got much trouble.

In the box where the dimmer goes there should be two of each wire, white, black and bare.
Join the two whites together and tuck them into the box.
The bare wires and the green screw all go together. Cut yourself a length of spare bare (ground) wire, marrette one end of this together with the other two bare wires, turn it round the ground screw in the back of the box and tighten it down, then join the other end to the green screw of the dimmer. This is a "pigtail" and it makes things easier in many situations. Tuck this into the box.
Last, join black to black.

Under the center console/dash you should has two connectors.

LARGER CONNECTOR

A Right Front Speaker (+) Green Gray
B Left Front Speaker (+) Pink White
C Right Front Speaker (-) Blue Gray w/ Black Stripe
D Left Front Speaker (-) Purple White w/ Black Stripe
E Ground Wire Black Black
F +12 Volt Ignition Wire Gray Red
G Power Antenna Wire 1 Blue (join wires 1 & 2
H Power Antenna Wire 2 together to this blue wire)
I Do Not Use

SMALLER CONNECTOR

J Right Rear Speaker (+) Red Purple
K Right Rear Speaker (-) White Purple w/ Black Stripe
L +12 Volt Battery Wire Blue w/ Yellow Stripe Yellow
M Left Rear Speaker (+) Black Green
N Left Rear Speaker (-) Yellow Green w/ Black Stripe

find the other end and you may use a wire connector or a wire connector
{ blue} push together clamp style or even just trim back the wires and twist together and use electrical tape to join them

You need to jump the neutral safety switch there was a plug you disconnected in front of the shifter it has either 4 or 6 pins, take the plug you pulled out cut it off of the old gear selector and plug it back in and strip the wires back, the wires are color coded so like colors usually go together. with a 12 volt test light ground the clip to a proper ground, turn the key to the start position hold on start and check for voltage at the wires you previously stripped, let go of key and voltage should stop if voltage is constant you may be on the reverse light circuit, keep looking for voltage that goes on only when key turned to start, when you find it look for the corresponding color ie green /white to green/ black etc, wire the 2 together and starter should crank over, if not try another one. you will also need to wire the reverse light switch from the new trans to this connector. stay away from brown wires as they are grounds on bmw and never hook anything but brown to brown unless you are 100 percent certain it hooks up that way