There are several AeroGarden models that operate with a pump (rather than an aerator/bubbler), and the pump setting does not behave in the same way in all models.
AeroGarden 7 pump models:
Your pump has a normal "off" cycle, meaning that it is not programmed to be "on" all the time for most plant selections. On many AeroGarden 7 models, the pump runs continuously only when the plant selection is set to Salad/Lettuce. Move the plant selection to the Salad/Lettuce setting and within 10 seconds you should hear the pump start. If not, lift up the water bowl just a few inches off the base, then reseat the water bowl back into the base. Often the pump contacts on the back of the water bowl and front of the light post are not lining up properly, and simply repositioning the bowl will realign the contacts and start the pump.
If the pump still did not start, try the self-diagnostic test: Press and hold the "Select" button on the base for about six seconds to start the test. During the diagnostic, all systems will turn on and off, one by one: the grow lights, the plant selection lights, the 'Add Nutrient' light, the 'Water Low' light, and the water pump. You should hear a faint hum and the sound of water gurgling when the pump turns on. If you hear the pump activate, then your pump is working and was just in an "off" cycle. You may move the Plant Selection back to the correct setting, and the pump will activate when it is programmed to do so.
If you do not hear the pump come on, continue with the next troubleshooting step: cleaning the electrical contacts that supply electricity to the pump.
If you have the Pro 100 model, the pump operates on a 12 hr on/12 hr off cycle for the first two weeks while in Germination mode. If you don't hear it running, it is likely in an off cycle. To test the pump: Move the plant selection to Strawberries, then press and hold the 'Select' button until the Strawberries selection light begins to blink, then release. You should now hear the pump start.
AeroGarden Harvest, Ultra, Extra models (with the Miracle Gro logo on the hood), and Bounty models operate differently. These models all have a pump connector cord that exits from the back of the bowl and plugs into the back of the base. Make sure the pump is plugged in securely before moving on to further troubleshooting.
Extra (with Miracle Gro logo on hood): If the pump is set to 'Germination 1/11' setting, the pump is running only 1 hour out of every 12 hour cycle (1 hour on, 11 hours off, repeat). To test the pump, use the Pump 'Select' button to choose the 'High Growth/24 hr' option. The pump should now start. You can lift up the Grow Deck/Lid off the Water Bowl to see the water pumping upward from the center of the bowl. The pump cycle should be set to High Growth after about 2 weeks, or once all plants have germinated.
Ultra: During the Germination the pump runs only 1 hours out of every 12 hour cycle, or 2 hrs in a 24 hr period. You can first check the pump cycle by pressing HOME then choosing 'More Options' then 'Garden Status.' Each screen on Garden Status will give you an overview of a particular setting. Press OK until you reach the Pump Cycle setting and the reading for the On/Off status. If the pump is in High Growth or 1440 on/0 off status, then it should be running continuously. Otherwise, it is turning on and off automatically as it should. To test the pump, you will have to change the pump cycle. Press HOME then 'More Options' then 'Custom Settings' and OK 3 times then 'Pump Cycle' (which will again give you the current pump cycle), then Customize Pump. Use the arrow up/down buttons to change the Minutes ON to1440 and Minutes OFF to 0. This sets the pump to run 24 hrs and the pump should now start. You can lift up the Grow Deck/Lid off the Water Bowl to see the water pumping upward from the center of the bowl.