I have little experience with appliances, but before getting a new washer, I was wondering what might cause a GE washer to be able to spin and fill, but not agitate. Could it be something that I could fix on my own? I hear and see it trying to agitate, but it kind of makes a whirring noise and doesn't move when it is on the agitate cycle.

Disconnect the power. If the wsher does spin but does not agitate, check the agitator splines. They may be wore out. Turn the transmission pulley in both directions If it will not turn in both directions it is bad. This is a costly repair even if you choose to do it yourself. Weight the cost of repair and age of unit vs new one. If the trans pulley turns fairly easily by hand, but the clutch drum is turning slowly or not at all under motor powr the clutch may be bad. Usually there will be a loud rattling noise. These are things to check out that could be causing your problem. Hope this helps you out. Good Luck