You want to know if you can use the HDMI cable for your TV with your computer as the input. The answer is no.
In simple terms, all color video starts out as RGB (red, green, blue). Each one is an actual video signal all by itself (although in just that one color).
Video is nice. It CAN make a picture. But your monitor or TV doesn't know left from right, top from bottom. So there also needs to be horizontal drive and vertical drive. Those are the two signals that synchronize the monitor to the video.
Now there, for the most part, is where VGA stops. Yes, there's SVGA, XGA, U-XGA, etc to describe the various resolutions, but that's unimportant. You're talking about hooking up to your TV. And your TV does NOT do RGB.
I know, you're wondering about those Compnent connectors that are also red green & blue. We'll get back to that.
Now, those drive signals for sync are combined into 1 composite sync signal. The green video is used for basic video called Luminance (which is just the brightness & contrast of black & white TV). The red and blue video is encoded into it's own signal called Chrominance (or essentially the color portion)and is just the color itself, now longer any video in it. Now, the color portion is combined with the brightness portion, which is then combined with the sync portion, so that they can all travel on one wire, or one channel.
In your TV, the sync is separate from the rest and sent to the synchronization circuits. The color portion is separated and sent to the color circuits. Here, it's interesting. Red and Blue are decoded and sent to each of their own circuits. Anything remaining HAS to be green, so that's sent to its own circuit.
Meanwhile, the actual green is just B/W. And the red, blue, and green COLOR is applied to the appropriate areas of the B/W video. (The color is just color ONLY, in a code. It has no video itself.) So, while the TV station takes each tiny part of a TV signal and combines it into a complex single signal, your TV deconstructs it back into its individual parts and displays it on your screen.
Here's the problem. Red video, as it was originally created, is no longer red video. It's just red color in the proper area of a black & white picture. Same for blue. And green, too, really. So no matter how much we try to preserve quality, all that encoding and decoding degrades the image.
Now comes VCR's. When recording a VHS tape, it never does combine the luminance and chrominance. They each go on their own tracks. So why combine them out of the VCR, just so your TV can UNcombine them again? And so S-Video was created. It takes separate color and B/W information and sends it directly to the proper circuits in the TV without combining/separating them. Color is just a little bit better now. Not a lot, but a little bit.
Then along come DVD's. Lots more room on them critters. So you don't even need to squash red and blue together on one channel. There is a separate red color information (remember, it's been coded so that the original video is no longer there, just the color coding). And there is a separate blue color information. Whatever is left, again, HAS to be green, which is also being used as the Luminance information. And you have Component, which uses Red, Green, & Blue connectors to distinguish them from each other. The color is now better quality than S-Video, but still not the original full VIDEO colors.
And that's what goes into your HDMI cables. So what makes them better, or more expensive, than Compnent cables? The use of a SINGLE cable instead of 5 for connection between your DVD and your TV. It makes less of a mess of spaghetti behind your entertainment center or wall mount, and it also reduces the potential for picking up cross-talk, or interaction between cables and other unrelated cables back there.
But, unless your TV is specially designed to be used as an RGB monitor AND TV, it will never be able to accept VGA, no matter what cables you use. You'll need a VGA - HDTV converter box which contains electronics to do the conversion.