Ok, so you're getting Time Warner's broadcast basic service, which is 20 analog channels.
Does your TV only find only the analog channels (2-20) or does it turn up a few digital channels (36-1 WCNC, for example)?
I'm going to bet you have 22 analog channels and a half dozen QAM channels available to you. Thing is, finding a box that'll handle QAM and analog AND output to HDMI isn't going to be easy.
The iView box you have is only going to pick up clear-QAM signals. You have to set it to scan for QAM rather than ATSC. It will not pick up your 20 analog channels. Check the settings and try it, again.
NOW.. if your television isn't picking up digital channels at all (no 36.1 or 36-1), then the digital channels from TWC are all scrambled and you'll need a box from the cable company.
Walking the fine line between jaw-dropping and a plain ol' yawn.