1. Boot your computer into Safe Mode. To do this, repeatedly tap the F8 key after your computer completes the POST but before Windows starts to load. If done successfully, you'll be brought to an Advanced Boot Options screen where you should select the option called "Safe Mode" seeing as how you shouldn't need any networking capabilities or the command prompt.

2. Navigate to Device Manager. One way of doing so:
(i) Click Start then "Control Panel".
(ii) Locate and double-click the "System" link (easier to find in Classic View).
(iii) Navigate to the "Hardware" tab.
(iv) Click the "Device Manager" button.

3. Locate and expand "Display adapters" bullet.

4. Select and delete any existing display adapters.

5. Close any open windows and proceed to reboot your computer normally.

6. Hopefully you'll be able to get in Windows without your monitor going blank, and at this point, search for and locate the most current driver put out by the manufacturer of your GPU.

Unless you already know the make and model of your GPU, I'll have to download and run HWMonitor to find out that information (just download, extract, and run: no install required). Depending on the manufacturer of your GPU, go to either one of the following links:
ATI
NVIDIA

Note: Some manufacturers, such as Dell, either won't let you or don't want you downloading drivers direct from the GPU manufacturer. If you're unsure about you're PC manufacturer's policy, you can contact them for such information and that concerning where to find the most current video drivers.

7. Locate, download, and install the appropriate video driver for your machine. Close all actively-running programs and open windows before starting the installation process as they may cause an error with the install and result in a BSOD.

8. Reboot your computer as necessary/if prompted.

Note: While this is a pretty safe, straight-forward, and known "fix" for issues like yours, you should proceed at your own risk.