I recently installed a new motherboard with a Radeon graphics card in it, but whenever I plug the dvi/vga converter onto the monitor cable, it instantly goes into power saving mode, and I don't even have to plug it in the computer for this to happen.
It will come out of power savings if you plug it into the computer! If it is not connected to any source of output from the computer (does not detect signal) it will go into power savings.
You should plug in the adapter and cable with everything turned off!
As rolli59 stated - Your monitor will go into power saving mode when it is no longer receiving a signal from your computer. Since it is not connected to anything but the adaptor (does not povide a signal until plugged into the computer) then your monitor will go into power saving mode. You have to plug the three together, monitor, adaptor, computer, to get everything to work.