If your washer doesn't spin or agitate on either the delicate or regular cycle, check these:
Selector switch
Clutch assembly
Drive motor
Selector switch
If your washer has a selector switch on the control panel, make sure the button for your selection is pressed all the way in, or set properly.
Clutch assembly
Many GE®/Hotpoint® washers use a clutch and an automatic shift lever. This assembly is quite complicated. If there's a problem with it, you probably should contact a qualified appliance repair technician.
Drive motor
Many washing machines have multiple-speed drive motors. Though it's uncommon, the drive motor may work fine on one speed but not on another. If the drive motor has failed on one speed, you need to replace the entire motor.