Is the server one where you can run programs? If the server page is written in PHP (maybe others, but I know a little PHP), you could fire up an app in the background that opened a socket connection to the Arduino (build the Arduino app using the Chat example as a starting point).
Or you could run a webserver on the Arduino, and POST the text to it. The example code supplied with the Ethernet library may not support this, but I'm working on an update to Ben's Webduino framework that will. It should be ready before the weekend. Wanna be a beta tester for it?