Will you
only ever be running the TV, DVD, Sat' tuner, & computer??
If so then you can use a fairly small (~300W) inverter. In that size category and considering that you want to hard-wire and are running AV equipment, my suggestion would be the
MorningStar SureSine.. It is a pure sine wave (PSW) inverter and rated at 300W continuous and 600W for up to 10 minutes. They can be purchased from online retailers for less than $200.
Cheers
-Mark