Make sure that the Inverter is on UPS mode. There are 2 modes UPS and Wide-UPS. Wide UPS is for bulbs and fans & such type of loads and UPS mode is specifically for PC. If you connect a PC on Wide-UPS Inverter, then when power fails PC may restart rendering the purpose of inverter useless.
Secondly check the VA rating of the Inverter and how much load it already has and how much it can handle.
Watts = VA × Power Factor