When it's not below freezing, where does the water discharge? It may be frozen there or somewhere inbetween.
If you can't get it working I suggest buying another pump just to prevent a flood and get through the winter. Not another sump pump but just a small submersible pump typically used to drain pools and such. Connect a garden hose with then end going to a sink so the water goes into your sewer system. If you were to put then end outside it would likely freeze.
This one is good (Wayne is a good brand): https://www.amazon.com/dp/B0009X8O2E/ref=psdc_554568_t3_B00ZTRG7EW
This is the same but with a water detection float switch to turn on automatically https://www.amazon.com/dp/B00502AIUU?ref=emc_b_5_i
Although the description doesn't say so these pumps can run dry for a while. Water is used to cool the motor. They're not terribly expensive so if you burn one up, oh well.
Not a long term solution but will avoid a flood. Hope it helps.