One day I was driving our 2001 Buick Century Custom, and I noticed that the odometer wasn't lit up. At first I thought that a bulb was out, but this instrument panel cluster (IPC) is completely digital, so there are no bulbs in those locations. The odometer/tripometer is all LED segment displays. It wasn't until later I noticed that the transmission indicator was also unlit. This can be dangerous if you think you are in park and are actually in reverse and let off of the brake. My wife and I kind of just dealt with the absence of indicators for a few months until I finally got around to fixing it.
Since there was no erratic behavior of any sort, I figured this was just a faulty discrete component somewhere and set out to look for it. If certain parts of your IPC are not illuminated when they should be, there is a good chance that this is what's wrong with it. I have found lots of people who had or are having the exact same issue, and this procedure fixed them all!
Step 1: Helpful Tools
While this isn't a precise list of what you may need, it should get you started on the right track.
To remove and open the instrument panel cluster I used:
Socket Set with Extension - Primarily a 7mm Socket
Battery Terminal Wrench - Equivalent to a 1/4" socket in most cases
Auto Carpet Plug Puller - Pliers and a flat head screwdriver should work as well
Flat head screwdriver
To fix the IPC I used:
Soldering iron and solder
4 x 150 ohm resistors