If you don't know how the dirt got in your tank I sure don't either.
The tank is not what holds all the water, it simply holds the solids while the bacteria feast on them. The water goes out into a drain field that allows the water to soak into the ground. Since your ground is totally saturated, it doesn't want to take any more.
I'm sure there are other ways to empty the tank of dirt than removing the entire top, I'm just not sure what they are. Sorry.