Solar energy system design and calculations to power a computer
As Daniel said, this is an enormous amount of power for just a computer. Not your standard computer, no? Most laptops use less than 50 watts, in comparison.

Background: I built a system that runs off of solar 24/7. The load is 150 watts. I'm using 800 watts of panels, and 6 deep-cycle lead acid batteries (Capacity about 100 Ah each). With consecutive days of no sunlight, assuming full charge on batteries, it can run 60+ hours before failing.

Your system needs to be able to charge batteries AND support your load. The advantage is you are only running 8 hours a day, and I will assume those 8 hours will occur during the solar day. With your load, I would start with 2000 watts of panels and a battery bank of 1000Ah. 

With a 500W load, at 12V: 500W / 12V = 42 Amps. 1000Ah batteries / 42 Amps = 24 hours runtime (fully charged batteries, no sunlight)

2000 watts of panels: Considering your location and weather, expect no greater than 75% efficiency for 5 hours of the day. 2000*5*.75 = 7500 Watt-hours generated per day.

7500 watt-hours generated - 4000 watt-hours used =3500 watt-hours left for charging your 1000Ah * 12V = 12,000 watt-hour battery bank. 

I am not including other efficiencies you may run across, so take this as a best-case scenario. I STRONGLY SUGGEST trying to reduce your load. 500W is HUGE! Building the system I described above will cost you a pretty penny too- between $5000-10000.