There is a lot of questions associated with that actual display which may come into account here. Those will come later.
To answer your first question: Yes, digital (HDMI/DVI/DipsplayPort, etc.) typically looks slightly better than analog (component). But, it depends on the video signal itself and the source content.
I can say that my home system, which was entirely analog for years, looked no better at all when I switched it to a digital system.
But, the reason to switch to digital is because of HDCP (copyright protection) and all the manufacturers dropping their component video output connections.
So, while I didn't see any significant improvement, I did get access to all the new gear which only had HDMI connections on it.
NOW... The bigger issue.
Your TV in this example is a rather ancient CRT rear projection TV that likely came to market very early on in the days of high definition TV and the days of digital television.
It is important to note that CNET lists the DVI input as a 'PC Interface' on their website. It was common for TV manufacturers to have PC inputs which were completely incompatible with standard video resolutions, which were often 480i, 480p, 720p (HDTV), and 1080i (HDTV). As well, these digital input didn't support copyright protection standards (HDCP).
But, some did.
Finding the manual was easy enough, and Sony DOES indicate that the DVI connection actually supports copyright protected material.
Even better, is that page 15 indicates that the DVI connection isn't for PCs, but it is for video equipment.
Worth noting, most modern PCs can put out a video signal that is compliant with video standards rather than PC standards, so most PCs will work with most TVs these days.
Page 8 of the manual indicates that it does support digital formats of 480i, 480p, 720p, and 1080i.
So... WOW! Looks like you may be good to go if you hook up a HDMI/DVI cabled device to your TV. Still, not saying you will see one bit of overall improvement to the video quality. But, you can do it, and I certainly would encourage you to start heading that direction.
Even more important to image quality on a CRT Television is making sure you have the image converged properly on screen. Get into the manuals and such to do your best job on that. I'm sure there is a ton online about calibrating a rear projection television. If the image is blurry, that's a key thing to do.
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