No doubt check the vacuum selonoid in middle of firewall near bottom of windshield either the vacuum is broken cracked dryrotted or the switch itself is bad it makes a fast clicking sound clllick cliick fast Or more than likely make sure your 4 whell drive is engaging my 99 gmc did same thing it was dryrotted cracked hose right at the nipple to selonoid on firewall. My 4wd lights didnt come on no codes thought 4 wd was working when it wasnt fixed hose and 4 low 4 high worked again with no clicking also check relays in glove box theres 2 or 3 fuel pump relay 4 wd actuator relay etc... And make sure that your vacuums are connected to transfer case there are 3 vacuums hvac vacuum to switch tramsfer case into 4wd and and a return. Line. Theyre located on driver side of transfer case hoses come from top of tranny so hard to see look for a triangle black rubber with 3 hoses comming off it

 

I fixed the cracked vac line at the drivers fender/ firewall and it has been 600+ miles and no problem yet. Very happy,,
I will pass this along to all I know that have a blazer.
thanks to all,