It would help if you post a circuit diagram and the code.
You need to get quite a few commands correct to get the EUSART to work and if any is wrong, you tend to get nothing at all and no indication why not.
What you can do is split things up as much as possible.
Write some test code to send a single character from the PIC regularly. You can then monitor the 5V signal with a 'scope or even an LED at a pinch. If stuff is being sent, check the RS232 levels. A 'scope lets you look at the waveform and lets you see if you have the right baud rate, number of bits etc.
You can check that you have hyperterminal working by connecting the RX to the TX signals, and turning the echo off on hyperterminal. With no link, if you type something, nothing should appear on screen. With a link, you should see what you type. You can do that test at either RS232 or 5V levels.