Proper sump pit water level?
The water should not be that high in the sump. It should be down to around the 2-3" level inside. This is what I'd call a safety margin which allows the pump time to rest should there be any sudden surge of water coming in from the drain tile or where ever else it might come in from (only other place I can think of off the top of my head would be the A/C drain, but you wouldn't get a surge from there). If a pump has to pump continually without resting, it will burn up the motor faster due to heat build up. 

There are two things to test. First, find the float switch which should turn your pump on when the water gets deep enough (it should be a ball floating in the water somewhere, maybe under the drain pipes). Rattle it around and see if it will turn the sump on. If it was stuck under the pipe, it may just need to be dislodged. If you rattle it around and the pump does not kick in, it could just be bad float switch, which you can get a replacement for if the main power cord runs through the check ball cord (hard to explain, but there would be a plug within a plug as it plugs into the wall). 

The second thing to check is if the pump itself is good (if the check ball does not turn it on). If there is the plug-in-a-plug situation as I described above, pull the two plugs out of the wall socket, pull them apart, then put the pump one (should look like a regular plug) back into the wall and see if the pump turns on. If it does, you can get a replacement float switch and you should be golden for the mean time. If it doesn't, you'll need to replace the pump.

Unless there is a longer manufacturer's warranty on a pump, you should replace them every two years anyway. I would bet this one has not been changed for quite some time. It gives a little piece of mind in doing so. As well, if you do not keep the maintenance up on your pump and the a flood ensues where the pump could have handled the difference, the insurance company might not pay for cleanup and repairs, so this maintenance item is a must in my house.