Can differential cause truck not to go in drive but will reverse?

A malfunctioning differential is unlikely to be the sole cause of a truck not going into drive but working in reverse. While a severely damaged differential *could* theoretically prevent forward motion, it would usually affect both forward and reverse gears. The symptoms you describe suggest a problem elsewhere in the drivetrain.

Here are some more likely culprits:

* Transmission Problems: This is the most probable cause. Issues within the transmission itself (e.g., broken linkage, internal failure, low fluid) could prevent forward gear engagement while leaving reverse unaffected.

* Driveshaft Issues: A problem with the driveshaft (like a broken U-joint or a disconnected driveshaft) could also prevent forward movement.

* Transfer Case Problems (if applicable): For four-wheel-drive trucks, a malfunctioning transfer case could prevent power from reaching the front or rear axles in drive, but not in reverse.

* Shift Linkage/Cable Problems: A problem with the mechanism that connects the shifter to the transmission could prevent drive from engaging.

In short, while a severely damaged differential *might* contribute to the problem, it's far more likely that the issue lies within the transmission, driveshaft, transfer case (if applicable), or the shift linkage. You should have a qualified mechanic diagnose the problem properly.