4x4 Problems

[Lowered13]

I just picked up a 1977 Chevy K10 about a month ago and have just had the first significant about of snow fall. I went to get out of the driveway and onto the road and i had a hard time getting out even though i locked the front hubs and had it in 4hi and tried 4lo. When i looked just the right rear wheel had been spinning for traction. So it seemed like my 4x4 wasn't working. What could be the problem here? Is it working right and it just to much for the truck or is something wrong with my truck?

I am pretty sure the truck is all stock drive-train and sense it is a manual it should have the gear driven np205 transfer-case.