Originally Posted by dmatch
Actually, if the OP has component output, as he indicated, that is HD when tuned to an HD channel.
There are PVRs made by Hauppauge (same manufacturer as linked to by ctdish above) that will record from component input. $150-$160. Requires a computer. I've never used one but I bet someone here has. The input would be analog HD quality on HD channels and the storage would be encoded digital (H.264).
You may be out of luck trying to find one, but if your cable box does Component-Out, there's actually a self-contained box by AverMedia called the EzRecorder Plus (not the EzRecorder 130, which does HDMI capture) that could be what the OP is looking for. It does scheduling (in a minor way, just standard one-input record-what's-on like a VCR), it has an IR blaster to tune the channels, and captures without the use of a PC. Only component (which is why I turned it down years ago, needed SVIDEO) but it could help.
The AverMedia Game Capture HD 2 box also does Component capture, but it doesn't have the IR blaster for changing channels.
Alternately, there's the old Monsoon Vulkano boxes, which I have tried and unfortunately have little good to say about. They were promising as recorders (you could use your PC and a guide to schedule recordings), but as a set-top box, you couldn't watch a recording while recording and it was woefully underpowered and out of date even in 2010. Still, a Component recorder, and if you use a separate playback device then maybe it'd be OK for you.
(*Keep in mind that we're assuming there's no Macrovision copy-protection on the Component-out signal. Given that the SD isn't protected, maybe the HD/P signal won't be either, but it's possible one's clean and one's protected, and if it's not clean then it's no good as a DVR.)
It might feel like your options suck given that there's no awesome single DVR solution (a WinPC recorder is doable BTW, investigate that if you can arrange for it,) but to me you're actually in a good position if you can capture Component, as most of us are stuck with cable boxes that only spit protected HDMI signal. Hang on to it, and give some of these odd boxes a looksee.