1996 chevy blazer will not go into 4wd hi but it will go in to 4wd lo. when you push the 4 Hi button it just flashes and then does nothing.

The major components to this system are a shift control motor that is mounted to the transfer case, and a shift control module that is behind your center console. since the transfer case is still shifting into 4wd lo, the shift motor is still moving somewhat, so the most likely cause is the shift control module, but there isn't an easy way to troubleshoot between the two...

Is it really going into 4-wheel drive low? Or is it just going into low range. Probably low range 2-wheel drive. I had the same problem and I disconnected the battery for about 15 minutes. That reset the system. I hooked the battery back up and my troubles were solved. Pushing the 4 wheel low button activates an actuator in the transfer case. Pushing the 4 wheel hi switch activates a pneumatic actuator under the battery tray. If resetting the system by disconnecting the battery doesn't work, you might have an air leak somewhere going to that pneumatic actuator.