This is a very common problem in S14's and can be easly solved. There are a total of 3 bulbs that illuminate the controls. 2 of them are the same and have a short base while the third bulb has a longer base which illuminates the fan speed knob. They should only go for a couple of bucks and change at the dealership. Here is a little walkthrough.
1. Gain access to your climate control unit by removing the trim and vents around it. Grab the bottom corners of the trim piece and pull out then up gently. There are four metal clips that will pop out with the trim. Be careful as the clips are secured to the trim piece by plastic tabs that can break easily. You can keep your hazard and defrost switches(and security light if you have alarm) connected to their harnesses and move the trim out of the way. I like to disconnect them so I dont have to fight with them later on.
2. After removing the trim piece, you can clearly see the four screws that hold the climate control unit in place. Once unscrewed, pull the climate control out.
3. Disconnect the two harnesses out of the control unit. I find that a small flathead screwdriver helps with this step.
4. Now using the same small flat head, carefully pry the back panel off of the control unit. Once panel is off, this is were it gets tricky. There are three plastic tabs coming through the circiut board that secures it to a second board. Using needle nose pliers, carefully squeeze the tabs to lift the board out of the control unit.
5. Once the first board is out of the way you will see the second circiut board that has the bulds attached.They have brown bases and can be removed with a phillips head screw driver. One is located on the top of the board, and the other is located at the bottom of the board. Use a phillips head screwdriver remove the old bulbs. Reverse this step to install the new bulbs.
6. The third bulb can be accessed by removing the fan control module. First, remove the fan knob with some needle nose pliers. Careful not to squeeze too hard as the plastic can break. Simply pull the knob out. Next using some small flatheads, pry the retaining tabs that hold the fan module in place. There are tree of them and can be tricky because they have to be lifted at same time and you only have 2 hands. Once you have figured out how to pry the tabs up, push the module out. Once the module is out, you can clearly see where the third bulb is located. This is where the bulb with the long base is located. Install new bulb and reverse steps. Module slides in place and push knob back in.
7. At this point you can reconnect the two harnesses that plug into the unit the verify that everything is working. If the bulbs are not coming on, recheck the bulb connections.
8. All you have to do now is reverse what you have done. Reconnect the first board to the three tabs. Then put the backing plate to the unit on. Reconnect harness to unit and secure unit with the four screws. Plug in your defrost and hazard switch harnesses and then simply line up the trim piece to your dash and firmly push the trim into place.
If my car wasnt at the bodyshop, I would have included pics, but you should get the idea once you start.
Thats it in a nutshell.