My computer is connected to LCD monitor by D-sub VGA and to a HD projector by DVI to HDMI. The only way I can get the computer to Startup with both displays connected is to disconnect at the DVI before I do a Shutdown and then I have to Reconnect before the next Startup. If I do not disconnect before Shutdown, then the next Startup gets to just before the Desktop would appear at which point the monitor goes black and pops up a "No signal" message. The graphics card is a GeForce nVidia 6600. There is no such problem if the projector is connected to the DVI using a DVI to D-sub convertor (i.e. analog.)
Thanks to everyone who tried helping with this problem. After much to-ing and fro-ing and trying this and that the card maker (Gigabyte) concluded that there is a compatibility problem between their card and this projector. Further down the track I will get a different card. For now I am using a d-sub to VGA converter on the DVI port and that works very well.