After dealing with this issue by adding a circuit dedicated to the sump pump, it has been very dry in my area. The sump pump hasn't kicked on in the month or so since the circuit was added. I wasn't worried...
However, the last week has been a wet one. Today, especially, has been near flood conditions to the point that they are closing many local schools. I still have not seen or heard the pump come on.
The sump pump power runs into the power cord from a switch, which then plugs directly into the dedicated circuit. The switch cord connects to a float set up in the sump pit, along with the pump itself.
The sump pit is a 25+ gallon pit with several drainage lines feeding into it at various levels. It has standing water in the pit, which I, as I understand things, does not necessarily indicate a problem. However, the water has risen above the highest drainage pipe, to within six inches of the lip. Still, the pump has not switched on.
I tried manually running the pump, and it operates fine, draining fairly quickly - half an inch or so in under 60s even during a moderate amount of rainfall. So my concern isn't that there are problems with the pump. Rather, I am concerned about the switch.
I do not see the float anywhere in the water. How high can the water get before it is certain that there is a problem?
Note that my fiancee and I are leaving town on Saturday to get married. We will be gone for two weeks. More rain is anticipated, so if I need to replace the switch, it must be tonight or tomorrow.
Edit to include pics:
This is what the pit looks like currently:
This is the water-level of the pit. The brown line on the stick marks the water-line. The paint-can is a full-size paint can, used to show scale: