Technic Rough Terrain Crane (42082) doesn't move After first book, crane won't roll if pushed. If this normal. I know when you free soon one wheel, the other will go opposite direction, but when I try to spin all four in one direction, it locks. It this normal until motors are functional?
Motor is only being used to operate the crane, not to drive the model. So driving/pushing shouldn't be blocked at any time. I suspect there will be an issue with position of differential - if placed incorrectly both axles will spin opposite directions. And if placed on the ground the model will simply not move.
Check steps 169 and 268 in instructions booklet to compare and confirm the position of differential housings in your model.
Step 169 has this picture:

Step 268:

Further step 273 has this picture showing that both differentials should be facing opposite directions:

It is also important to check the placement of the gears if they haven't been pushed too hard against any liftarms/beams and are not jammed.