Call for a septic company vacuum pump out service if theres a plug of solids at the valve or drain, which would allow a trickle as you described. If you are certain the valve opens. , vacuum will suck out the blockage. Then, if you have the dreaded poop pyramid break it down with a stick or a flexible piece of 3/4" elec. BX cable if your drain is not straight down into the tank. You may have to call for a pressure clean out to break down the pyramid.
Educate everyone about sufficient use of water and whats acceptible to flush.
