Without getting to technical, all computers (laptops, notebooks & desktops) have switched-mode power supplies to run all the various components within like disc drives, motherboard, monitor, modem etc. Switched-mode supplies run at efficiencies of 85% or better especially if the input voltage (220-240vac) is sine wave in frequency. Modified square wave/quasi wave power inverters have at best an efficiency of 60% due to their linear circuit design. They are cheap to manufacture, cheap to buy and should only be used for lighting, soldering irons and other resistive loads and power tools without electronic gear boxes. These inverters are rarely used in the UPS industry as they are considered too messy in output and unreliable for backup power systems especially with computers. They also interfer with anything containing a clock like microwaves, VCRs, DVD players/recorders, digital alarm clocks and so on.
The ticking sound you heard is most likely due to insufficient power entering the power supply from the inverter - ie the inverter doesn't have enough grunt and as the power power supply needs squeaky clean AC power it will go into overload trying to cope with the AC from the cheapy inverter. The overload is caused by the power supply circuit trying to start up to supply power to the laptop.
The simple solution is buy a sine wave inverter rated to at least 150 watts. This type of charger is kinder to your charger/power supply which could burn out if used with an inferior cheapy modified square wave inverter which you seem to have tried .
If you need more info PM or email me. I have been involved with DC-AC power inverters for over 20 years and use them in solar power systems I design and supply.
Good luck.