This is difficult to troubleshoot. Bummer.
Headlights and brake lights are on different circuits, and do not even use the same fuse. So don't look for a connection between the two.
> we accidentally pulled out part of a fusible link that was located near that battery, im not sure what it does but im sure we cant fix it.
The fusible link is the 'main fuse'. It supplies ALL the power to everything inside the car including the ignition starter switch. So the first thing is to re-connect the fusible link.
I recommend that you don't just run out and buy a new switch. Instead, determine what is wrong first.
> I tried starting the car up and then it didnt start either.
So headlights work, but not these?
* brake lights
* tail lights
* starter
What else? Does the dash come on when you turn the key to IG?
If not, use a voltmeter on the Fuse Box. Does it show 12V anywhere?
If IG worsk, but START doesn't work, remove the switch (one or two small screws on the back of the Lock Cylinder) and you'll have it free.
It looks like this:

Test it with an ohmmeter, continuity setting -- or with an old fashioned "test light". A good multimeter is only $20 at Sears. The wiring is detailed at
Tech: Ignition SwitchBasically, you'll test for continuity (0 ohms) between S and B terminals whenever you move the switch to the far clockwise position. Use a medium screwdriver to turn it.