how do i set up a minimal webserver, that serves only one page on all requests?

Giving this answer for the entertainment value mostly, but you could use any super-server (xinetd might do the job, too) and make it run a simple script for every request on port 80. The script would wait for a blank line on standard input and then print a prepared static response. Not sure how much more lightweight you can get.

For example, if using DJB's tcpserver (I find it easy to use for such trivial tasks) you can do:

$ tcpserver 127.0.0.1 1080 sh -c 'awk "/^\r*$/ { exit }"; cat answer'

And in the answer file you can have:

HTTP/1.0 200
Date: Fri, 02 Nov 2012 16:05:54 GMT
Content-Length: 15
Content-Type: text/html; charset=utf-8

This is a test

You can get as creative as you want.

And here is how I test it:

$ wget -q -O - http://localhost:1080/
This is a test

UPDATE: For anyone seriously considering this, for a realistic use of tcpserver you are better off starting it like this:

tcpserver -H -R -l $HOSTNAME -u $(id -u nobody) -g $(id -g nobody) 0.0.0.0 80 sh -c 'awk "/^\r*$/ { exit }"; cat answer'

By default tcpserver looks up information about the incoming connection and -H (do not look up the remote name in DNS) and -R (do not look up remote info with ident) will speed up responding to incoming connections. -u and -g will drop the privileges after receiving the connection on port 80, and you will have to start it as root to be able to listen on port 80.

And of course, make sure nothing else is listening on port 80.

Presumably this is prompted by the answer to your earlier question.

Why not (temporarily) apply a redirect rule in Apache to point everything to your sitedown page? (and if you do it via a proxy request rather than a redirect, then any PHP script at that location will be able to read the requested URL). You can swap in a different config without losing anyrequests using a graceful restart.