Problems with the drawers opening and closing are usually the result of overloading the drawer or trying to pull or push them at an angle.
If the drawer has too much in it, it can affect the operation of the drawer. For example, if it is too heavy it will pull too much against the guide rails that the drawer slides in and out on and will not slide smoothly. Also, if it is too full, an item could be catching and preventing the drawer from opening or closing.
For smooth operation, the drawer should be pulled straight out and pushed straight in. If it is pulled or pushed to the right, left, up or down, it will catch against the guide rails and not move. It can also come off the track or damage the components that allow for the easy opening and closing of the drawer. Be sure not to pull or push the drawer at any kind of angle, but rather only straight.
If any part of the drawer is broken or missing, this could prevent it from opening and/or closing properly. If this is the case, the broken or missing components will need to be replaced.