I have a 6 year old Dell Optiplex GX620 Small Form Factor Pentium D 2.8ghz with 3gb of DDR2. I put a $25 Radeon 5450 video card in it (Even you can do it, and it takes about 5 minutes). It depends on what you want to do with it, but it works fine for streaming and playing back video or playing DVDs.
I don't know what's required for the HD Homerun.
Put it this way. That Pentium D is a stronger processor than a brand new Atom or E-350.
I used a 512gb HIS Silence 5450, but any brand should be fine. Buy whatever 5450 card is cheapest. Sometimes they're under $20. You WILL want to put in a new video card.
I wouldn't sink a lot of money into it, but it is certainly worth a $25 upgrade.