the cold water comes out very slow but the hot side works just fine the filter screen looks clean could this be the water pump even thow the hot side works ok?
Your model number seems to be short several digits.
A Kenmore is usually 3 digits, a period and then 8 digits.
Sounds like the water inlet valve needs replacing.
It is possible that there is a problem with the cold side of the water valve.
Turn off the cold water tap.
Undo the hose at the machine and run some water into a pail, to be sure cold water is reaching the machine.
Sometimes hoses can de-laminate internally and reduce water flow.
Undo the hose at the tap. Some hose sealing washers include their own screen filter.
If OK, then odds are it is the water inlet valve.