IIRC lagcount is the equivalent of frametime.
ie player.x := player.x +1 * lagcount should work for you when using dxtimer.

Alternatively, when using your own gameloop (for example in the application.onIdle event.) the method I wrote above works.

Here's some sample code too (note: I haven't actually compiled it so it may contain a syntax error, but I'm sure it'll get the point across)
Code:
procedure mainloop();
begin
  finished := False;

  gameStart := GetTickCount();            // Get Time when demo started

  while not finished do
  begin
     LastTime := ElapsedTime;
     ElapsedTime := GetTickCount() - gameStart ; //Calculate Elapsed Time
     ElapsedTime := (LastTime + ElapsedTime) div 2;
      
     {.. your other stuff in here...}
     player.x := player.x + player.xspeed *  ElapsedTime 
     {.. your other stuff in here...}
  end;
end;
That avatar of yours is freaking me out by the way
Wait until you see the next one