Converting DVI to HDMI is it worth doing or just b

I ran a high quality DVI cable through the wall.
Should I bother getting adapters to HDMI for this cable or run a new HDMI Cable.

Thank You
If you do not need audio on the cable and you are not having any video problems, there's no need to run a new cable. In fact, when my in-wall HDMI cable failed, I switched to using the in-wall DVI cable with HDMI adapters rather than do the hard work. No problems at all.

This is related to the above post and please forgive me if it sounds stupid. I have a pre/pro with DVI. It also came with an accessory box for DVI to HDMI. Now if my TV is not an HD model, then the box is irrelevant, I assume, and I should just use the best video connection (component, S or whatever) that my TV has, right?