Broken headlight switch

Recently purchased 1998 Aurora with following symptoms:
Rotary (twighlight, sentinel) switch is broken, will not respond at all.
Dash lights do not come on at all.
Tail Lights (taillights) do not come on at all.

I was wondering if 1. broken switch would cause all problems? 2. If so, where can I find the switch, and how to replace?

Are you referring to the twilight sentinel control on the dash left of the steering wheel or the headlight switch on the turn signal stalk? I've never heard of troubles much with the twilight sentinel switch, but it's easy to pop out and should be pretty cheap. By the way, that switch doesn't have much resistance to it. It just rolls back and forth aside from a detent at the bottom to turn the sentinel system off.

The multifunction switch (cruise, headlights, turn signal) is damn expensive on the other hand.

What do you mean exactly by the rotary switch not responding at all? Do you have no headlights at all either, or just that you can't get them to come on automatically? All that control on the dash does is determine the length of time the lights stay on after the car is off, at least if it's anywhere in the on position.

I very well might be mistaken, but I don't think either of those would cause all your dash lights and tail lights to not work. I'd check al the fuses. There is a panel inside the drivers door on the side of the dash. There are also two fuse blocks under the back seat that have lots of fuses and breakers. The back seat just pulls up from the front. Those should be the first places to check.

If you don't find anything there, you could have a loose wire harness behind your instrument panel thanks to careless disassembly, or just a broken wire.

I don't know about the brake lights other than it was recently suggested that the switch down at the brake pedal might be the culprit. Just search for tail lights on the forum here- it wasn't that long ago. If you haven't, you might check both bulbs. It's doubtful they've both burned out, at least not without some other cause, but it's worth a look...

The switch (if you are refering to the twilight sentenial switch which it sounds like you are) you could probably find in a junk yard. Or go to the dealer or gm-car-parts.com or gmpartsdirect.com. The part will be extremely easy to replace. You can pull that piece off without removing any screws. It just pops off. You might have to use a little force but don't worry. That is the way you are supposed to take it off. I've taken mine off a ton of times. And then there will be one or two wire connectors you will remove. Then put the new one on the same way you took the old one off. It shouldn't take you more than 5 minutes (and that is if you run into problems which you won't). Simplest job in the world. You could just try replacing that and see if it fixes the tail lights. I would think the sentenial switch would be in the same circuit somehow. And seeing you need to replace the switch, just replace it and see if it fixes the tail lights. If it doesn't, then at least you ruled that out and it had to be replaced anyway. But if that doesn't fix the tail lights, you need to get a hold of a schematic of the tail lights and troubleshoot it by finding where you have power and where you don't in the circuit. Then replace whatever is breaking the circuit. (Did you check fuses and the light bulbs?)
But I just checked gm-car-parts.com and gmpartsdirect.com and I couldn't find it. But anyway, you would be better off just finding the car in a junk yard and getting it that way. It would be a lot cheaper.
But something else I just thought of, it might be possible that the wires behind that plate just came loose. Maybe you'll pull that piece off and the wires will be loose or just not connected at all. Wouldn't that be nice?

My 98 Aurora just got out of the shop for VERY similar reasons- It's probably the multi function headlamp switch. Which is actually the whole entire turn signal stick with millions of wires coming out the end and going into a plug that plugs in somewhere in your steering wheel or dash. I could be wrong about your car but I was told that this is extremely common with 98 Auroras to have this go out.