I have a '97 Chevy Blazer. It has the electronic push button to change to 4high and 4lo, however when the 4hi button is pushed, both 4hi and 4lo lights flash as if the system can't make up its mind. Then when the 4lo button is pushed it will engage. I forgot to mention that when 4hi is pushed the lights flash, a clicking sound is made, and it then returns to 2hi. Someone suggested disconnecting and reconnecting the battery cables, like rebooting your home computer.
Your Blazer is equipped with the "Selectable 4WD" electronic control system which engages the transfer case without the use of a manual floor-mounted shifter. Disconnecting the battery may temporarily clear trouble codes stored in memory, but it most certainly will not fix the problem. The fact that 4LO engagement seems normal and 4HI does not would indicate a failure in the 4HI circuit. The push button switch sends a signal to the Transfer Case Control Module (TCCM) which utilizes this along with other data in order to send the appropriate command to the Motor/Encoder unit. The Motor/Encoder is an assembly mounted to the transfer case that actually performs the mechanical engagement.
To properly diagnose the system, specific terminals at the Data Link Connector (DLC) must be jumped to display one of four possible trouble codes at the shift select buttons, along with performing a step-by-step functional test. Causes can range from a poor electrical connection to a mechanical failure within the transfer case. Sources tell us that the Motor/Encoder assembly is the most common problem.