No break light at all

get yourself a tester to see if you are getting power to the light socket, have someone push on the brake petal and use the tester to check for power. If no power, you have a broken wire somewhere between the rear lights and dash [fuse panel] check for corrosion in bulb socket. try to find the wire along the frame to the rear lights for any breaks in the insulation. electrical is one of the hardest problems to solve, good luck.

Your solution is a new combination switch,It also sounds like the hazard are activated and is non operation interfering with the brake light,but either way the solution is a combination swith

Bad brake light switch. It's just above your brake pedal under dash. Small plastic switch w/a couple of wires. Easy fix.

Since these are all electrical, I suggest you look at the fuses. I am sure you will find one burned out. I would guess that you replaced the bulb while the power was on, and that is not a good idea. It is easy to blow a fuse by doing that. If you put the bulb in wrong, it is possible it may keep blowing fuses as well. Make sure is it seated correctly, if this is the kind that rotate.

ck light bulbs.

check fuses with a tester. just because they look good can be missleading

Could be the break light switch whitch is usually found on the break pedal lever (just above the break pedal)..
If that is it - should be not to hard to replace..

It's the bulb. There are two filliments in the bulb. One is for when you turn your lights on and the other is for breaking and blinker flashing. When the break filliment goes bad it causes the blinker to flash very rapidly. 100% the bulb. Change it and all will be good again. P.S. if it were a fuse none of the break lights or blinkers would work.

If the 2000 Saturn SL2 is the same as the '99 SL2, then your tail lights bulb is the same bulb as your break light bulb. Now they are dual bulbs, just like your head lights. So just the same way that your brights can work, but your headlight lamp be out, or vice versa, is the same with your break lights. So replace both bulbs and you should be good to go. I just had to replace both mine, one was a tail light out, and the other's break light was out, either way, same bulb. Also, check your manual for the light, or take the light out when you go in to get new ones. I found that for some reason there is some confusion on the bulb in this make in model.

Do you know if the brake light bulbs are working? (are the bulbs good?). (the bulbs have two parts, one for brake lights the other for running lights)
If the third brake light bulb is working the brake lights should be with good light bulbs.