If the operating phase has the biggest impact, then it could make sense to buy a new appliance rather keeping your old one "for a long time." If your old one is super inefficient, then buying a new, more efficient one could, over time, make up for the added impact of manufacturing it.

What Umbra (and most of the world) miss is that what's good for conserving electrons ain't so hot for your health. The short explanation: CFLs, most other electronics that use inverters and variable speed motors create prodigious amounts of "distorted" electricity, which, due to an outdated electrical distribution system, flood into the environment -- and your household wiring. Think of it as converting rooms into low-power microwave.
Longer story: Industry spend billions annually to deal with this problem (i.e., improving power quality) but the rest of us remain completely ignorant. On the bright side, the proliferation of electronic gizmos certainly has the potential to mrarkedly reduce human overpopulation...
The Russians figured it out decades ago. Search for "radio wave sickness."

What about those units that project onto your wall? Wouldn't they be the most efficient because there is no screen to power?

I was wondering how projectors fared as well, but you have to take into consideration the bulb. Projectors use 150-200 watt bulbs that typically need to be replaced every 1000-2000 hours. So if you're talking just power to run, the projector probably wins out. But when you consider the cost of new bulbs and the disposal of the old ones, an LCD may be a better option, both economically and environmentally.

We gave up on our tv a year ago and catch watch we want to see on hulu and our netflix subscription on our laptops.

If you use earphones, the experience on a laptop is pretty good.