Welcome aboard.
While the transfer case is actually in 4LO, if the switch is NOT in 4LO it will flash the indicator to let you know it's going to try changing things. That's why you're seeing what you're seeing.
4LO may be stuck because of a bad servo on the transfer case, but it could just as easily be damage inside (bent pawl, for instance) preventing the transfer case from changing back to normal gearing. You could try (preferably on a loose surface like dirt/grass/sand/gravel) turning the car this way and that as you slowly move forward and back again to see if it unsticks.
If it doesn't, there are two possibilities I've heard of:
1) Servo failure. Now this might just be a relay in the engine bay too - you'd need to check those. The transfer relays are marked inside the distribution box (not sure which one in that model). If the relays are all intact and operating, you could see if there's a voltage being sent to the servo or if the servo works when it's removed from the transfer case.
2) Physical fault inside the transfer case. What usually happens is a pair of pawls move and engage the front drive shaft (2HI -> 4HI) and then a gear change occurs with a 180 degree turn of the servo as the case moves from 4HI to 4LO. If something is interfering with the gears, even if it's a fragment of metal (like a broken tooth from the chain that's dropped into the wrong spot) it could cause this.
End result might even be the search through a bunch of wreckers for a replacement transfer case, so if you want to know "worst case", give a couple of wreckers a call and ask them what they'd charge for a transfer case.