You want a battery to power a computer for a few months, with no external power?
You need something along the lines of a rack of UPS batteries, at least, and don't forget that rechargable batteries slowly discharge over time, so how long you can run the computer off battery power would get shorter over time.
Sorry, I should have explained that better. I have some 'pico' computers about the size of a credit card. They run at about 600mA idling and a bit more at full load. By high capacity, I don't mean anything near the capacity required to run a full desktop for a few months.
I guess it is more equivalent to running a mobile phone for a few months?