As to why the inverter didn't work with the laptop charger, I have seen that happen.
A lot of inverters are sold as "modified sinewave", which is more like a square wave with every second pulse negative. The waveform has about the right RMS voltage, about the right peak voltage, and about the right Volts-seconds so that conventional transformers don't saturate. As a result, most loads will work fine.
However I've seen a laptop power supply that simply did not turn on when connected to one modified sinewave inverter. I think that the power supply detected the periods of zero voltage between the pulses as power interruptions.
For that, I bypassed the problem by connecting the laptop charger input to the DC voltage that the inverter produces, before it is chopped into the modified sine wave. That meant opening the inverter, messing around with lethal voltages, and having an IEC lead with DC on it, what would have damaged quite a lot of loads, but it did run that laptop.
I would go for a direct 12 V input laptop charger if I did it again.