Cold water trickles into the tub while it is being filled up

The hot and cold water supply hoses that connect the washer from the water supply faucets on the wall to the water connections on the back of the clothes washer usually have filter / sediment screens within there connection fittings at the end of the hoses, these will collect dirt,sand, calcium deposits, etc.,when they trap enough of these materials they will plug up and restrict the flow of water into the clothes washer. Turn off the water faucets at the wall, and you should do this for both hot and cold hoses, disconnect the hoses from the washer and the water faucets, look into the hose ends and pull out the screens and clean them out by running water and what ever you can use to clean them completely!!!!!
Now look inside the water connections on the back of the clothes washer,where you screw the hoses on the washer, and check to see if there are filter screens in there, if there is, remove them and clean out completely also, then reverse the removal process and reconnect the hoses, makeing sure to connect the hot and cold hoses to the right connection on the back of the clothes washer!!
Try filling the washer with water to see if you have corrected the problem.
Make sure hot and cold hoses are correct on the back of the washer!!!!
GOOD LUCK !!!!!!