cold water not pumping through ?

On most washing machines there are two electric water valves
one for the hot and one for the cold, in most machines there is a double cold electric valve, the valve is the actual white plastic threaded section that you connect your water pipes to the machine, try your machine on a rinse programme if it fills at a reasonable speed then that part of the valve is ok, if on a cold wash programme it fills slow as you suggest, then you just need to replace the complete cold valve, just unplug the machine from the electric and take off the top of the machine
to accesss the water valves, turn off the cold water and remove the cold water pipe, make a note of your electric connections to the valve, and remove the internal water pipes
from the valve to the machine, and simply replace the Double cold valve in a reverse proccess, you should be able to buy a cold double valve from most washing machine repair stores, or purchase one on line.

Ken jenkins
September 2007