2003 Toyota Canmry xle 4 cyl. automatic 41k

This is my mother's car. When she uses the remote starter the engine turns over continuously but will not start. I recently noticed that while the car is turning over but not starting that if I just barely put the key in the ignition the car starts with no problem. I don't put the key in very much at all it just seems to make contact but the car starts. Does anyone have an idea of what the problem might be? Mom is 83 and needs her remote start for the winter. Is it worth the cost of troubleshooting and repair or would it be cheaper to install a new unit?

Thanks J