Hi, Brian,
First of all, pls check your hardware whether the USB translator accept RS232 logic voltage or just uart logic voltage(0~3.3V).
If you still have issue, I suggest you connect the TXD0 to a scope and have the TXD0 output characters continuously, and check if the TXD0 can output signal.
Anyway, pls follow up the procedures to initialize the uart0.
1)TXD0/RXD0 pins assignment:
P0[0]/TXD0/PWM1
P0[1]/RXD0/PWM3/EINT0
PINSEL0&=~(0x0F);
PINSEL0|=0x05;
2)set the baud rate of uart0

3)write the UART0 Transmit Enable Register to enable transmitting.
4)write the U0THR register.
5)poll the bit 5 of UART0 Line Status Register, repeat (4)
Hope it can help you
BR
XiangJun rong