I'm in the same boat as you. I've been looking at product descriptions for HDTVs all day, and I'm ready to take a nap now.
I did find the Panasonic CT-27HL14.
According to the specs I read, it will remember it's last input and power on automatically. I've also read that it is either 27" exactly, or 27 and 1/8" wide. Either way, it may be able to fit your cabinet if your cab is already built.
I saw a cheapo Advent (I think) 27" HDTV, but it was over 30 inches wide, if I remember right.
In fact, it seems like the only HDTVs smaller than 27 inches were either lcd, widescreen, or had speakers on the sides, making them too big.
Anyway, that's what I know. And since it's been a couple of weeks since you asked the question, maybe you've found something else? If so, would mind helping me out. I'd love suggestions, so I can stop searching through tons of tv's that aren't appropriate.