As small as they are, I wonder how much of a stretch it would be to just start putting commodity Arm 1.1ghz dual core CPUs and a build of android - basically a cell phone - inside any and all TVs these days?
Just pop it in there in and amongst all the other circuitry, stick an SD slot on the side of the TV for folks who want more storage...bam, Mr. and Mrs. Livingroom can phone up Jane and Johnny while they're at the university, play Angry Birds, look at photos, etc. all on the TV, no screwing around with a dedicated computer. Just use the remote.
At commodity prices it could hardly cost more than a few bucks to outfit each TV thusly.
Something like this then:
http://www.raspberrypi.org/http://www.wired.co.uk/news/archive/2011-01/20/raspberry-pi-computerTo be honest, whilst I'm a big fan of the Raspberry Pi project, as it sets out to improve computer education in schools, I absolutely abhor your idea. Sorry for wording this so strongly, but in essence all you're doing is increasing the space for consumption, rather than re-engaging people with the power of computing. The idea isn't to dumb down the interface to give people the basics that companies think they want, it's far better to give people tools and let them find ways to use them for their own benefit.
This Henry Ford quote, related to the innovation of the affordable motor car, kind of touches on what I'm trying to say:
"If I'd asked customers what they wanted, they would have said "a faster horse"."
If you give people devices that just let them consume, then after a while consuming is all they'll expect their devices to do. However, if you give them devices that allow you to freely create as easily as consume, then you've offered them liberation. So don't bury computing power behind lacklustre interfaces, give it a chance to be all it can be.