You could do it with a deep cycle marine battery (I recommend an Optima sealed battery) and a trickle charger.
Run the amp while you're on the computer, and let the charger recharge the battery while it's not in use.
I've got an Optima battery in my Jeep Cherokee, and have run my 1420W total sound system for 5-6 hours in the park without killing the battery

(it's an 800cca model battery).
Sound system specs
Sony CD/MP3 deck powering 4 Pioneer tweeters @50W each
Pyramid 500W pro series w/ 2 10" Pyle Drivers
Pyramid 240W pro series w/ 2 Pioneer 6x9's
Pyramid 240W pro series w/ 2 Pioneer 5 1/4's (back doors)
Pyramid 240W pro series w/ 2 Pioneer 5 1/4's (front doors)
The subs and 6x9's are in a custom built & tuned box in the back.
WOW, more power than I originally thought! (I just did the math

)