It's hard to judge how hard you're hitting your power supply. On "idle", it's pretty low. At other times, it'll get close to 100%. To be sure your batteries will hold out, I'd take 75% of the rated power of the power supply in the PC, plus 100% of the power consumption of the monitor, plus any other peripherals (printer, scanner...).
If you're using an inverter to convert the 12v to 230v, reckon on about 90% efficiency in that.
My guess would be that you're talking somewhere between 300 and 500 watts at 230 volts, so about 25 to 40-ish amps from the batteries. If your power outages are several hours at a time, that's a lot of amp-hours, so some very large batteries. Then, there's the question of how fast they will recharge when the power comes back on.
I'd be more inclined to go for a llittle generator. There are some very nifty little 1 kilowatt ones available for very reasonable prices. You then have the advantage of being able to have a lamp running too, so you can see what you are doing.