Jimster:
I've also replicated the problem using a diode between 5v and analogue input 3. When tested with a digital multi meter it shows around 4.2v but stil 1023 on the serial monitor.
As well as a diode, you need a pulldown resistor connected between the pin and ground. When the DMM is connected, the DMM acts as a pulldown resistor. Disconnect it and the pin will probably float up to 5V.
Check that the Aref pin isn't shorted to anything, and that Avcc is connected to +5V.