You're probably better off just buying one from the store. WalMart, K-Mart, FRY's, RadioShack, and lots of other places sell them. I have seen them on sale for $30.00 or less.
You don't want to risk permanently messing up your computer hardware by using a homemade inverter. If you want to work on a homemade project, you'd be better off building a DC/DC power supply than your own inverter.
And yes, having a big transformer that outputs a square wave is WAY less efficient than a commercially-made inverter. Most of the newer ones use high-frequency switching techniques and thus generate less heat and are smaller & more efficient than the older style units. Plus some computer hardware has enough trouble dealing with the newer style inverters, let alone a square-wave monster from the past