I recently had my new dryer installed. However, the tub spins but there is no heat. This is a brand new dryer

I have a 4 prong dryer chord. Does the fact that 2 of the wires--a green and a white wire are both connected to the grounding (green screw) have an effect on the dryer not having heat?

I'm surprised that the ground (green) and neutral (white) are connected to the same lug since you do have a four-wire system. Nonetheless, that isn't causing your problem. Since the drum spins, you have power to the unit (at least one of the two live wires is connected). Since it's new, it should be under warranty, contact whoever installed it and tell them to come and fix it. It's possible that the heater element is faulty.

If you want to do some trouble-shooting yourself, check for power between the two power pins and the neutral (white). You should see approximately 120 Volts (AC) (make sure your meter is on the 250 VAC scale) on each line. You should see 240 VAC between the two live wires.