I suspect that trying to run the flat panel without the kvm switch might not fix your problem. I suspect that the problem has to do with the settings in your /etc/X11/xorg.conf file. YOur flat panel doesn't use the same settings as your old CRT. You should try to find the range of values for your new monitor's horizontal sync frequency and vertical refresh rate, before you start, then you can use expert mode. It will give you a cleaner xorg.conf file.
Try to start your computer in recovery mode (the second entry on the boot menu). You will get a full screen, black and white console. Login with your name and password and then enter the command
sudo dpkg-reconfigure xserver-xorg
. You will have to enter your password again. Then just use the defaults until you get to the part about configuring your display. I you're using expert mode, this is where you get to enter your horizontal sync and vertical refresh values.