Trying to convert a three-prong dryer cord to an updated four-prong plug connection. I took the old plug off and re-installed the proper new wires according to the package instructions. However, the old green ground wire is still connected to the dryer somehow. Don't think it should be cut. The old ground wire was connected off to the side (kind of on the body of the dryer). The new plug has its own ground wire. Not sure if I could connect the two ground wires together and then place it in the respective location. Tried to get assistance from someone at Home Depot but was on hold for over a half hour. Please help if you can. Thanks.

Yes, any green ground wire can be connected.

Word of caution.

Older 3 wire dryers connected frame ground to the Neutral wire from the source.

When you convert from a 3 wire to a 4 wire, you must disconnect the ground jumper on the dryer frame frame from its connection point on the electrical block, otherwise you will be connecting neutral and ground together.

The easiest way to do this is to either disconnect the ground wire from the frame and then connect the ground wire from the cord directly to the frame. The other alternative is to cut the dryer's ground wire, leaving enough wire to splice the new ground wire to it and then cap of the section of ground wire that goes to the electrical connection.