97 Blazer 4x4, No 4wd Lo

[ScottyBoy]

I have a 97 blazer 4x4 that I've been piddling with. Something seems to be wrong with the 4wd Lo gear. When I press the transfer case switch (button) the 4wd Hi button will light up when pressed and I can hear a noise under the shifter/console area, sounds like a solenoid engaging. But when I press the 4wd Lo button the button doesn't light up steady lit like the 4wd Hi button does. It just starts blinking when I press it, and I don't hear the solenoid engaging like when its in 4wd Hi. I have no clue what do do from here or where to even look. What could be wrong and what should I look at or try and test?