If you don't already have one, I'd head down to the local hardware/homegoods/electronics shop and pick up a multimeter. First thing to try is to use the DC voltage setting and check the leads going to the pump when you think it should be running and verify that it's getting 12-ish volts. The main thing to figure out first is if the pump is burned out or if the problem is "upstream" of that.

I don't think you really have a problem with the solar panels or the battery, because it looks like from the controller display that your battery is fully charged to around 13 volts... which should be fine. But I'm making assumptions about what that display means.

Possibilities that occur to me:

• The pump motor is burned out
• You have a defective lead going to the pump (you can use the continuity mode on the multimeter to check that)
• A transistor blew on the charge controller (one possibility is that the controller is not designed for driving motors... when a motor turns off, it can generate a big spike of power back to the controller... if the controller is not designed to handle it, it could damage the circuit).

EDIT: On the multimeter: you don't need a super fancy one. Even the cheapest should have DC volts and something to do a continuity check. A more sophisticated one will be more useful for other projects, but it's not like you need an expensive meter that measures down to the milliohm and can whistle the Star Spangled Banner.