There are reasons cheap TVs are cheap. This is one. :)

I have run into this before as well. Not much you can do about it except use 2 remotes or heaven forbid the actual power button on the TV itself....assuming it is not too cheap to have one of those....I think it is a UL requirement though.

I know DirecTV boxes have HDMI control. Does this work to power on the TV? I usually turn it off out of habit so I have not tested it.