This, by far, is the most common problem associated with our cars. It mainly occurs with 1985-88 cars with the base or electronic instrument clusters. Here's the likely scenario: the dash lights won't come on at night, and usually the digital speedo won't light either. (Some people have also reported that the headlight switch smells like it's burning, or it actually does smoke). And as a result, you have to drive around shining a flashlight into your speedometer to see how fast you're going at night. Sound familiar? Well, it CAN be fixed, but you need to inspect a few things first.
First and foremost: Make sure that all the little light bulbs didn't burn out of the dash (including the two in the speedometer module and the two in the radio, if necessary). We know, its common sense, but you might want to check it out anyway. This requires removing the cluster, or at least taking it out of the dash far enough to get your hand back there. For cars with column shifters, be careful of the gear indicator cable on the bottom of the cluster—that can easily get bent or broken if you're not careful. There are 4 T-20 Torx bolts in each corner of the cluster—remove them, and it's essentially loose. If you need to remove the whole cluster, you must uncouple the wiring harness(es) on the back of the cluster. Squeeze both sides of the harness at once, and just pull out.
Second, you could have a bad fuse or circuit breaker. We've had that happen before, and it drives you nuts until you discover that out. Over time, circuit breakers and fuses can wear out just like any other mechanical part. Since there's always power going through them, day or night, it makes sense. That's a cheap fix and you can have the questionable parties tested if necessary.
Third, one or both of your wiring harnesses for the dash cluster could be loose. That's kind of uncommon but well within the realm of possibility. And it's a free fix.
Fourth (and probably most important): Have you installed a radio lately, or removed and replaced the stock one? If so, that's probably your problem. The wiring behind the radio can get pinched very easily due to its proximity to the back of the radio. The main culprit is a light blue wire with a red stripe; that's the one on the same circuit for the dash lights. It's for the light in the radio, clock, and lighter panel/ash tray. When that wire gets pinched, it causes a short in the system, and since the dash lights are on that same circuit....no more dash lights. Even worse, if the fuse doesn't blow, then you've got power overload running through the car, and the common gateway is the headlight switch. This can cause electrical feedback into the switch and make it smolder, spark, or burn. It's no fun to have a headlight switch burn up on you halfway to work.
How to solve it? You must find out for sure if that wire's getting pinched. (There's another wire that can also cause the same problem—light green with a yellow stripe). Best thing to do is remove the radio and start moving wires out of its way. If you try in vain to wiggle wires around and still can't solve the problem, then there's the last resort: tracing the wires back to the fuse box, cutting both, and hooking up only the one that goes to the dash lights. The fuses you'd look for are either the #5 (15A, light blue) or the #13 (5A, tan) positions (please refer to this page for a full fuse panel reference guide). That should solve the problem once and for all, but it's only recommended as a last resort. That should get you back to getting normal dash lights, and your flashlight can safely reside in the glove box again.