I have another suggestion for you
Instead of running your desktop when power is gone all you need to do is plug in your router and moden into your ups and run your laptop on your laptop's battries which should ideally last for more then two and a half hours as you said its a new laptop.
In my opinion your ups alone should keep your modem and router running for more then an hour or so if the battries ar in good shape and even two hours if its a large battrey.
If you have an inverter at home even if its single battery then you can use inverter's power to power up your modem and router and both of them put together dont use more electricity then a small bulb say 20-30 watts at the most if I am not wrong ( some one please correct me if I am wrong)
This way you should be able to stay online for as long as your laptop's battery lasts and even longer if you plug in your laptops charger to your inverter's power as a laptop's charger is normally 60-80 watts which is not a lot even for a n inverter with a single battery.
If staying online is very important for you and is productive enough for you to spend some money on it then I suggest you get an inverter with 3-4 exide tubular batteries and you would never have to worry about back up again... not atleast for the next 4 years or so as those battries last more then 4 years.