I have found a way to indicate the network activity via the LED.
I had the idea that I could use the parallel port pins for that. So I played a bit with this and I got a little program to run, which sets or resets a single pin of the parallel port. After that I wrote a small bash script, which parses /proc/net/dev and watches for changes in received and transmitted packets. If there are changes, the bash script calls the program which sets the specific pin on the parallel port (the LED) and resets it after 0.05 seconds. Result: a flashing LED.
I just managed to connect the other two free LEDs (LAN port 2 activity and system failure) to the parallel port. I'll see how I'll use them.