I had the same problem with my 2003 ford explorer. Replaced the shift motor on the transfer case and fixed the problem.
The 4low button blinks before it engages. The number of flashes helped my mechanic figure out what the problem is. Each flash represents a task.
Aftermarket part costs around 200 dollars and 100 for labor. Done for 300 dollars. You can also find used part for very very cheap and replace it yourself. Many videos on youtube that explains how.