Hello,
Given the voltage problems on your grid, no UPS will allow you to properly use your PC (the batteries from the UPS will never properly charge). Use a voltage regulator (AVR) BEFORE the UPS, something like this: http://www.apc.com/products/resource/include/techspec_index.cfm?base_sku=LE1200I&ISOCountryCode=de.
Your original 600VA UPS is also a little bit too small. Your system will need 350W DC power, so if your 850-watt PSU is of a decent quality (at least 80% efficiency, active PFC), you will draw from the grid 500VA. Adding the monitor, you are reaching the UPS power rating. If the PSU is old and inefficient (under 60% efficiency, passive PFC), the system only can easily draw 700VA from the wall.
That APC didn't work as it should or you were just annoyed by the fan noise?