My Yukon has same issue, but I never got my front shaft in, when u start mine , lights blink on the buttons and eventually they quit blinking and the red nuetral light comes on....all while driving down the road. I e been through all wiring and is all good, put in same part as u did and finally hooked scanner at the shop to it and cannot communicate with the tcase, long story short is the tccm( transfer case control module) is bad . It's like $350 for a reman and the fact I can't get my front shaft in means I'll need to rebuild tcase or replace it, I'm not spending that much cash on a tccm. Luckily I can get a donor tcase, buttons, and tccm for a non auto tcase ( mine has auto 4x4 and the donor only has 2hi,4hi,and 4lo) and u couldn't pay me to use 4auto anyways, it'll be worth my money to swap in another one. I was tempted to out a manual tcase in but didn't have a donor trans tunnel to cut and weld Into my Yukon. Hope my babbling helps ya out some , I'd point at the tccm being your issue. I'd check for power and ground at the tccm plug before replacing it tho, I believe there are a few circuits that power the complete 4x syatem. Also grounding points tend to rust and cause big issues too.
