The touch screen no longer works
Jamie, if the touchscreen really doesn't work anymore then this is a major problem. There are ways to make the Samsung Galaxy Q pick up/answer calls automatically when you get them, but you have to use an Android app.
It may be possible to use a Bluetooth headset and set it up so that all calls are answered automatically when it is connected to your phone, so you could look into that. Making calls via voice commands can be done through this as well.