The question itself relies on the variables of the computer. Because we know how much a solar panel system will collect as far as energy, and we know it doesn’t work at night, we have to figure out how much a computer will need to operate.
To find out how much the cost will be to use the computer, you pretty much use the following formula
The watts x the hours you use it x the cost per kilowatt per hour / 1000 = total cost.
That means that a great computer that is overclocked and used for high end gaming and an LCD flat panel monitor left on for 24 hours would take a maximum amount of energy. The power supply would probably be 200 watts so for about 24 hours a day you would have about 1,700,000 watt hours, or according to the formula, about 1700 kWh. If you pay a high end of thirty six cents per kilowatt hour, then you pay about $600 + per year for the energy wasted by the machine.
The same thing goes for a computer that doesn’t take as much energy, such as an iMac, and it goes to sleep when not being used. If this computer, which uses 105 watts, is only used about 2 hours per day, and only on business days, then you have only about 10 hours per week on it which means you have about 50,000 watt hours per year, or 50 kWh. If you pay a low end of about 15 cents per kilowatt hour then you pay about $5 a year.
The difference in $5 to $600 is huge, but the idea here is not to go based on the extremities above, but to see the difference between the two, and find out your middle usage to figure out how much energy you need to replace.
Now you have to figure out how many panels you need to operate that much energy per year. A typical 2 kWp solar installation (which uses roughly 12 m2 of roof) will produce around 1700 kWh of energy per year. This is by far way more than necessary. It is way too many panels to produce enough energy to push a computer even at high end and maximum usage.
Since for approximately 30Watts of power, each panel system costs around $225 you would probably need about 5 of these as a minimum not to mention any of the back end things you need to hold the power etc. However, being that well taken care of panels last from 15 to 20 years, the benefits of going off the grid for any given computer system, unless the household has more than 5 systems, is probably the best idea since butter on toast.
If a laptop is being used, then the amount of power consumed on a daily basis is by far lower than a standard PC. When booting up any computer, laptops included, the systems take more energy, however; when compared to a PC, you are looking at saving tons of money and only needing about 2 panels.