Strange RX Port Behavior

Unfortunately I'm at work so I won't be able to post an actual wiring diagram until later, but here is a written description (all wires are going from the module to the Arduino board):

Both Modules:
VCC --> 3.3V
GND --> GND
TXD --> Pin 0 RX (for Serial, for SoftwareSerial Pin 10)
RXD --> Pin 1 TX (for Serial, for SoftwareSerial Pin 4)