Since the check valve locks itself after you put everything together and start the pump, it might be because of the frozen or blocked pipe section on exterior. As soon as you turn the sump pump on, water fills up that blocked pipe and creates pressure that locks the valve as soon as the sump pump stops operating.
Besides freezing, the exterior section of pipe might be heavily corroded (especially if galvanized and partially buried under ground) to the point that blocks water flow. If the exposed, exterior section has no union you can take apart, I would get a pipe rubber connector with metal clamps (unfortunately they will corrode over time), and cut the pipe on exterior.
Disconnect sump pump power supply, disassemble section below the check valve and open the valve, cut metal discharge pipe on exterior approximately 12″ from the house wall penetration. After you put everything together, turn the pump ON to see if it’s discharging properly through the cut section.
If it is, your problem is wherever this pipe continues its run. It definitely shouldn’t go to the septic tank or not even near it if possible – too much water can cause it to malfunction. If everything works fine after cutting the pipe, just use that rubber clamp to attach short extension for now (try to keep it above the ground and sloped down).
When it gets warmer, run a longer extension away from the house. The relief hole below the well cover won’t hurt, and sometimes it does help. You can drill it when the pipe is disassembled / pulled out from the well. Drill it at the slight angle pointing down towards the well bottom.
Let me know if that helped