[w0mbat (Ian)]

Alex the first thing you need to do is measure the actual ac power draw of the computer. I would be shocked if it is more than a few hundreds watts.
From the small amount of info about the solar power system you have given you should not have a problem running the computer for reasonable periods.
I was once an agent for Rainbow Power. They are good people. If you give them the information needed they will give you reliable information in return.
Ian
PS
In my experience the switch mode power supplies of desktop computers (or any computers) do not require high quality power so should happily run on any generator or square wave inverter.