Hello Atomski,
try to use some delays
before your greeting, put the line PAUSE 500
and between the following line as indicated.
HSERIN 2000, No_Data, [Ser_data]
PAUSE 500
IF Ser_Data <> 0 THEN

Personally I had used the following and worked fine (for higher baud)

INCLUDE "modedefs.bas"

' ******* Definitions *******
' ------------------------------

DEFINE OSC 16 ' Define clock Oscillator Frequency at 16Mhz
DEFINE HSER_RCSTA 90H ' Enable Hardware USART receive
DEFINE HSER_TXSTA 24H ' Set Hardware USART parameters
DEFINE HSER_BAUD 9600 ' Set baud rate to 9600
define HSER_CLROERR 1
CMCON=%00000111 ' Make PortA digital

' ****** Initialise PORTs ******
'----------------------------------

TRISA = %11110000 ' Set PORTA status (Low byte=Output, for LEDs)
TRISB = %11100010 ' Set PORTB status
PORTA = %00000000 ' Initial state of PORT A
PORTB = %00000001 ' Initial state of PORT B


This might help ... I hope.