little pump isn't working
As Chris says, you should never plug a high current device like a motor directly into a pin on your Arduino. That motor is rated at 800 mA, which is more than you can draw from the entire 5V supply on the Arduino!

The digital pins are rated for 40 mA max, if I remember correctly. You tried to draw 20 times that much. There is a decent chance that you burned out the driver for that digital pin. I would try hooking an LED through a 220 ohm resistor and to ground and see if it still lights up when you send it a HIGH logic signal.

For a simple DC motor you should be able to use a high current transistor and an external power supply to drive it.

Edit:  If I were doing this I would use a logic-level MOSFET to drive the pump directly, plus a flyback diode. To use a relay, you will still need a transistor to power the relay coil, AND a flyback diode. Your circuit might look like this:



(Note that I made no attempt to pick the RIGHT kind of diode and transistor. Ignore the part numbers shown in the schematic. I just used the defaults.)