No, a DVI to VGA adapter will not work. (The TV is looking for the digital signal from a set top box. This is different from the analog signal on the VGA cable.) You need a converter. Your best bet would be a VGA to component video converter. (I am assuming that the Sharp TV has a component video input.) This page has some examples: http://www.ramelectronics.net/audio-video/video-converters/vga-rgb-hv-to-component-video/c10000-c11200-c11215.html?sorter=productname-en-asc
. Note a VGA to component video cable will not work. The VGA to component cables are for projectors that read the RGB signal. The component video signal is YPbPr.
Connect the VGA cable to the converter and the component video cable to the TV and the converter with the computer and TV off. Turn on the TV first and set it to the component video input and then turn on the computer. Then (assuming the VGA port is enabled - adjust in the BIOS if needed) set the computer's video output to the VGA port. (On my Windows 7 laptop, this can be done by right-clicking on the desktop. Choose Graphics Properties and set the display to the external monitor or both. Click Apply and then confirm the change (on the external monitor if using the single monitor). (VGA to Composite video converters also exist if you do not have an available component video input on your TV.)
If your computer is fairly new, you may have an HDMI port. Your TV may be able to read the signal with a DVI to HDMI cable. (It depends on the TV. Not all of them will read the computer's signal on the DVI port. Check the documentation for your model. TVs without a VGA port are less likely to support this feature.)
I hope this helps.