How can I control my Azpen Android Tablet with a broken screen without root or usb debugging?
You could get a USB-OTG cable, which allows you to connect USB devices to Android devices via the USB port (so long as the Android device supports OTG, which the A700 does). If you plug in a mouse you'll get a mouse cursor to work with; you could even use a USB hub to attach both a keyboard and a mouse if you want to type instead of using the on-screen keyboard.

You could also use the USB-OTG cable long enough to pair a Bluetooth mouse/keyboard to the tablet, then go wireless.