Great informative answer! Many thanks deweyzeph
Except that the figures given are too high. There is no way a desktop PC would draw 500W continuous unless you are gaming with a very powerful graphics card.
Also, laptops can draw around 30W. Check the power brick. It should have a wattage on there.
I would estimate your entire setup would be:
Laptop: 50W
PC: 200W
Router: 12W
Total say 300W rounded up.
All 3 use switched power supplies, so should run off a decent modified sine wave inverter, but you may as well get a pure sine wave inverter of around 1KW because I'm sure you will want it later.
204Ah x 12V x 80% efficiency x 30% discharge = 587 Watt hours of power.
So your two batteries will give you almost 2 hours of backup (587W/300W) and last many years at only 30% discharge.
But something to check is, what is the battery capacity at the current draw you are expecting of it. You can't draw 50A from a 102Ah battery and expect it to last 2 hours. Most batteries are quoted at the 20 Hour rate, in other words, it will supply a total of 102Ah over 20 hours (5 Amps per hour x 20 hours). But the capacity will be much less if you draw higher currents.
The datasheet will tell you the effective, lower capacity in Ah at the current rate you are going to draw (300W/12V = 25A). Look for the capacity at 25A. It may be only 80Ah or less.
This is all very confusing I know, but it is worth understanding to save yourself money in the long run by ruining expensive equipment.