Check engine light on and D4 light blinking. Car starts but transmission gears wont engage

Hello, there is nothing easy or inexpensive with what you are dealing with here. You'll need the assistance of someone who has experience diagnosing OBD-I Acura's and troubleshooting transmission operation. My biggest concern here is that the problem occurred "after I swapped engines". This could mean you have an incompatibility issue, a wiring issue, something left unplugged...endless possibilities. Whoever swapped the engine should double check each step of the process to check all wiring and components manipulated.

Sounds to me like the torque converter might have been mis-indexed in the oil pump, causing the pump gear to shear. This would result in no hydraulic pressure in the transmission. No pressure, would result in no movement. If the vehicle never moved after engine installed, but moved before engine was replaced, I would put my money on transmission pump failure. You can start replacing parts listed in the many forums on line, or you can save some money and pay a technician to properly diagnose your vehicles concern, and only end up replacing one part.