The dryer cord is a three wire cord, I am installing a new dryer outlet in the basement, the previous outlet wire was a 4 wire cable with ground attached to the metal box, I am replicating the same setup in the basement, I bought a romex 10/3 cable and a metal box, my question is do I connect the ground to the box ? the metal box I bought does not have a ground screw, can I use any screw to connect the ground to the metal box ? or should I use a PVC box instead in which case where do I connect the ground coming from the cable?
The risk with not grounding the box would be the hot wire touching the metal, and with no ground the breaker won't trip, this could result in it grounding through you if you touch the box (electrocution). Some outlets are "self-grounding" where no bonding wire is needed for the box. Check the outlet to see if it is self grounding. You can add a screw to the box for a bonding wire if not. After installation, check with a meter- one lead in a hot receptacle and the other lead touching the box, if the meter reads 120v, the box is grounded.
You should connect the grounding conductor to the metal box. You should be able to pick up a pack of grounding screws from any local hardware store. There should be a threaded hole in the back of the box, where the grounding screws should fit.
If there's no threaded hole, you can use a grounding clip.