2000 Blazer 4.3L LS, Push-button 4X4 problem

Hello everyone, I am an absolute moron when it comes to cars, so let me say that I will try to describe this as best I can and try to give me the "For Dummies" version of what you think is wrong!

In my 2000 Blazer LS, about 131k miles on it, the push-button 4x4 seems to be having a problem. Every once in a while (not very often, maybe once a month or less often), while you are driving, the 4Lo button starts blinking. As soon as you come to a stop and shift into Neutral, the transfer case automatically shifts into 4Lo all by itself.

If, while still in Neutral, you try to shift it out of 4Lo and into 2Hi, sometimes it will make the shift and other times it will revert back to 4Lo.

I've seen in other messages on this site that it might be the actuator on the transfer case, but if anyone has seen this happen before and knows for sure, please let me know!

Also let me know an approximate cost of parts and amount of labor involved. Doesn't have to be exact, but a rough idea would be great.

Thanks for this terrific site! It's great to be able to ask these questions without feeling as though it will cost a fortune just to sound like an idiot!