1994 Chevy Silverado

Do you have an electric shift or on the floor 4wd shifter?

It is likely that your interlock in the front differential has failed. If it's the factory original, it's a heat operated device that takes a few seconds to engage (at least) when you throw the lever into 4WD. I recommend one of the "instant on" replacement interlocks that have no delay. Installation is pretty easy except for tight access. Cut wire ties to free wires and electrical connector, unbolt old one, unplug and remove; bolt in new one, plug in and tie wrap up wires neatly so they don't catch any snarly stuff on the trail and you should be back in business. Good luck and I hope this helps.

Either there is a linkage problem to the transfer case, or the interlock, as mentioned, isn't engaging the front axle.