2002 explorer a/c blowing out of defrost and not dash vents

The direction of the air flow (dash/defrost/floor, etc) is controlled by vacuum going to the switch. There may be a vac line that didn't get connected or was damaged when they put the replacement engine in it. Check the lines on the firewall to make sure nothing is loose.

This problem sounds similar to the problem I had on my 2002 Ford Explorer. The vent control would not change the vent direction from front to defrost and such. Turns out the Vent Control Box control arm is made of plastic and broke so that it was no longer connected to the vacuum motor. You can easily determine if this is the case. Open the glove box and empty all of its contents. Then press in the sides of the glove box until it can be moved rearward and down. Look in the space behind the vent controls to see if the plastic vent control arm is connected to the metal vacuum motor arm. If not that is your problem. You may need to start the engine and move the vent control selector to see the vacuum motor arm move. It will move whether or not it is connected to the plastic arm. A dealer will charge $2000 for this repair because they will need to replace the entire vent box assembly. I fixed mine for next to nothing. I will share if anyone is interested. Note: The repair is simple but not easy as there is limited space to work and you can only get in there with one hand. Warning: There are really sharp metal brackets in there that will cut you if not careful. The fix is in the attached image. I fabricated a new metal bracket from scrap sheet metal using a di-grinder. The bracket is attached with a sheet metal screw about 0.63" thick. The pin is replaced with a bolt and self locking nut. I used an air drill to drill the hole in the plastic arm. Vent control works like new now.