PeterH:
I'm not familiar with that module, but it looks as if it has a uart and I assume that's the one that is expecting to receive your data. Does it have a uart? Is the Arduino connected to it and using the correct serial settings? Is the Arduino receiving "CONNECT" at the right time? The code seems to be sending the data over the Arduino's hardware serial port, so unless you have connected the Rx/Tx lines to the GPRS module's Tx/Rx lines, I wouldn't expect that to work. (This would mean you can't also use the hardware serial to talk to the PC; I think you would probably be better off using a software serial to talk to the GPRS module, if you can get that to work. Or get an Arduino with two hardware serial ports.)
The GSM module does have a UART. What do you mean by "Is the Arduino connected to it and using the correct serial settings?" I'm running it with the same baud rate.
I'm so sad. 