I have been trawling the Internet for ages looking for the solution as I had the same thing. Boot up in safe mode and all works fine through DVI. Boot up normally and you see as far as loading Windows 7, or whatever OS you are using, then as soon as it gets into windows you lose the signal. Also everything works fine if I use a DVI>VGA adapter, but the image is significantly worse than if I use DVI digital. Anyway, to cut a long story short the problem is that through some mechanism (in my case I had a GeForce FX card failure that caused this) the EDID data on the EEPROM chip in your monitor has become corrupted. You will need the full registered version of a tool called PowerStrip made by EnTech Taiwan to attempt to correct this. The trial version doesn't have the feature required to attempt this.
When it's installed and registered, shutdown your PC. Make sure you have connected the faulty monitor only using the DVI digital cable to the graphics card. Disconnect other monitors if you are using more than one. Boot up into safe mode (keep pressing F8 while booting up to get the option to boot into safe mode).
Start up PowerStrip and right click on the System tray icon. Go to Options > Monitor Information. It will probably just say the manufacturer is Microsoft and the Model ID is "Default Monitor" or something instead of your actual monitor details. At the bottom where it says Options, select the option to Update EDID. Follow the instructions to detect an EEPROM device, and hopefully it will detect you have corrupt headers and it will ask if you want to correct them. Select yes and follow the prompts. At the end it will ask you to restart. Hopefully you should be all good after the restart.
I used version 3.83 of PowerStrip for this and originally received an error saying "An EDID EEPROM was not found" when scanning for the EEPROM, but this is because this version didn't have support for updating the EDID on a Geforce 275. I tried the same procedure on a GeForce 6600 GT on my old PC and it worked perfectly.
If this doesn't sort out your problem you can try and locate a full EDID export for your monitor and use the same procedure to upload it, but there are some additional steps you need to know doing it this way, so read the full article that helped me resolve this at http://blog.komeil.com/2008/06/fixing-edid-dvi-monitors-no-signal.html.