Beatrix,

have you tried the simple test described here

Have you set the Baudrate on the PC-side correctly
and is "Handshake" set to none?

Could you post a schematic and your code (cut down to the RS232 part)

For a one-way communication (PIC --> PC) you definitely need only two wires:
PIC-GND to PC-GND and PTC-TX to PC-RX

Probably your PCs COM-Port doesn't work with TTL-Levels.
If so you would need to add a MAX232-type of Level shifter.