Your problem is the refresh rate on the computer exceeds the monitor's abilities.
The Windows logo shows fine because the Windows logo screen is displayed at 640x480 @ 60hz, which is a very basic setting. The desktop probably loads at 800x600 @ 60hz or higher, which could be an issue depending on the age of the monitor.
To fix this problem, boot into Safe Mode.
When the computer powers on, you'll see the initial BIOS screen with a manufacturer's logo or a bunch of information about your computer. Directly after this screen, the Windows logo probably appears. You'll need to tap the F8 key just a split second before the Windows logo shows up and a menu will appear. Try it again if it doesn't work the first time.
Navigate the menu using the arrow and enter keys. Select "Safe mode" and your computer should boot right up into a very ugly and limited version of Windows. Right click on 'My Computer' and choose 'Properties' from the menu. Click on the 'Device Manager' tab. Double click on 'Display Adapters' and right click on the adapter listed underneath this group. The menu should show an option to remove or uninstall it, please do so.
Restart the computer and it will boot into 'normal' Windows. Your resolution, refresh rate and color depth will be set very low (probably default - 640x480 @ 60hz). Change these settings by right clicking anywhere on the blank area of your desktop and click 'Properties'. Click the 'Settings' tab and adjust the slider to the desired resolution (at least 800x600) and select the highest color depth possible from the pull down menu (Usually 24 or 32-bit). You should increase the refresh rate to at least 75Hz, which you can do by clicking the 'Advanced' button in this window. 1024x768 @ 75Hz+ would be a good value for a 17" or greater monitor. Someone with poor vision may prefer 800x600 @ 75Hz or better.