In theory you can get 50ft out of an HDMI before you have to worry about attenuation/signal degradation and have to go for an active power solution. My guess is your cable is not up to the task of pushing a good signal. I've tried running that same kind of setup and ran in to the same imaging problems at around the 30ft mark. Get a shorter cable and see if you're hitting the same problems. You can get them for like $5 for a 6ft cable from amazon. If it comes up clean, it was the cable. If it comes up with the same issues, then you may have a faulty port on your video card.
If you're needing to be over 30ft away from your computer, you may want to look in to one of the NUC or small form factor computer and just set it up as an HTPC. You can get them for like $300 for an i3 or $500 for an i5 setup straight from big box stores like Bestbuy.