Okay, I've done lots of research and this is what I found. ALMOST EVERY converter box, including the one listed above is not HDCP compliant. What this means is that some HD content will be blocked. That kind of ruins some of the best parts of streaming. There is one product that seems to be of quality and good review, the HD Fury, but it is so expensive that you might as well buy a new TV, seriously. By the way, read reviews and watch out for knock-offs of that product.
Any cable that attempts to go from HDMI to something other than DVI is a waste. Like composite, component, etc. They won't work. DVI would work, but it is video only!
The best solution seems to be to go with a Roku 2 model or lower that has different outputs. Roku 2 has an A/V port (which the Roku 3 does NOT have) with which you can connect to composite RCA jacks (NOT Component). But beware of this. As far as I can tell, you can NOT use a STANDARD 3.5mm to Red, White, Yellow RCA cord. Many people have complained of this (and I have a great quality one right now at home MYSELF, that does NOT work). Apparently the 3.5mm plug is PROPRIETARY and I have ordered one from Roku and will update on this. Their website says they are proprietary but that did not stop me from trying like everyone else.
Quality will automatically be diminished by not using the HDMI cable, but the first generation HDTVs screwed up or were at least too late jumping on the HDMI boat.
Perhaps you should go with the cheaper Roku HD or Roku LT if your TV is so old that you don't have HD quality anyway. There is no reason to upgrade the Roku then just downgrade what it can do, just so that you can hook it up to your TV, unless you are planning on buying a better TV in the future.
Another option is to hunt down a Roku XDS. This DOES have a port that can split to COMPONENT video output (Red, Green, Blue). As far as I can tell is that Roku doesn't even make this one any more (they don't sell it on their own site). I assume the software will not update much for it. And as far as the cables, I'd buy them direct from Roku. They DO sell them (at a decent price) right on their site.
What I did was take the first unit I had, the Roku 2HD and used that in my basement with my older TV (mostly for kids and treadmill use), and installed the new Roku 3 on my main TV. I was hoping to utilize the headphones in the remote function on the treadmill, but oh well. The biggest loss is the picture quality. But the kids won't care anyway. As it stands, even the 2HD is not working. Hopefully the cord from Roku themselves will do the trick.
I hope my many hours of looking (grief) helps some of you.