I have a 3-prong dryer cord and I am trying to switch to a 4-prong. There is a white cord coming from inside the dryer attached to the ground screw. Do I leave that cord attached and also attach my green cord to the same screw or do I take the white cord off and just put the green one on? 
It would be best to get the full model number and then find a install sheet on the web, probably the Sears/Kenmore site. It should tell you how to change the line cord.
Kenmore numbers are 3 digits, a period and then 8 digits
I can give you some basic info.
On a 3 wire machine ground and Neutral are the same.
On a 4 wire machine ground is separate from the Neutral. It is true earth ground.
On a 3 wire there is usually a jumper wire that runs from the terminal strip Neutral/white (usually the center connector) to the machine frame.
When changing to a 4 wire this jumper is removed.
The line cord Neutral/white is connected to the terminal strip center connector (usually).
The line cord Ground/green is then connected to the machine frame.