When I turn on the dishwasher, I can hear the motor run, and when I turn the dial I can hear it change cycles, but it doesn't fill up or spray water. Is it the pump? Okay, more info - since no water is coming in at all, maybe it's the water inlet valve? I am sure that water is available - when I unscrew the hose, water pours everywhere. I really need to fix this thing - my hands are getting chapped from washing dishes!

I cannot find your model number.
Are you sure that it is not a 04BB instead of a 0488, see the following.
Replacement parts for General Electric GSD3620Z04BB Dishwasher | AppliancePartsPros.com

There can be several causes.

I would check that the float (Item 490 in Section 1) is activating the float (overfill) switch(item 490 in Section 1)
Sometimes due to crud etc. it can get stuck in the up position so the unit thinks it is already full.

If OK check that the fill valve (Item 744 in Section 1) is getting 120 volts when it should be filling.

If it is then either the fill valve is toast or the screen filter on the input side is plugged.
Remove the valve and check/clean the screen filter.
If it is clean replace the valve.
If dirty clean it. Do not permanently remove it as it is there to keep crud out of the valve which would hold it open and cayuse a flood.

If there is no voltage check for voltage (120 volts) across the overfill switch.
If there is voltage then the fill switch is toast.
If there is no voltage then check actross the valve and switch combo (they are wired is series) if there is no voltage then odds are your timer is toast.