A frind has a lexmark x1100 printer/scanner.
It has a "copy" button, when pressed it will scan something in and
instantly print it. (This is not a hardware solution, the button just
opens the lexmark scan tool and does not work when the PC is off)
The printer part is broken (actually it never worked that well), but
there is another printer connected to the same PC (running windows
2000)

Can I somehow reconfigure that button on the lexmark to use the other
printer, so that copying a dokument is as easy as it was before?

You will not be able to configure the buttons of one printer to
execute that function on another printer. However, if the scan
function is working on the printer which wont print, you can scan the
document to the pc and then print it on the other printer.