the odometer and the light to show what gear im in has stopped working can this be replaced
first check to be sure no fuses have blown, You need to have odometer changed by proffesional as there may be some legal issues otherwise ( odometer rollback ) and if your car is overheating first check your therostat, it may be stuck and need replacing, if not that check your water pump, if the water and antifreeze are not circulating properly it will cause overheating. if this is not problem and you have oil leaks be sure the heads are not warped ad the seals are all good. hope this helps.
The odometer light fails because of 4 resistors on the circuit board have burned out. If you know how to solder, and feel comfortable taking the dash apart, it's about a 20 dollar fix, 150 ohm 1/2 watt resistors and you can get them at radio shack.
https://www.youtube.com/watch?v=rtRINop3gE8 The above link is the best one available. Tells you how to take dash off and purchase new resistors and to solder the repair. Dash installation is reverse of removal.
https://www.youtube.com/watch?v=rtRINop3gE8 The above link is the best video available showing how to take dash off and instrument cluster out and make repair.
Looking for a Used Century in your area?
CarGurus has 1,070 nationwide Century listings starting at $3,300.
Search Buick Century Questions
Buick Century Experts