Either there is something obvious here I can't see or I have one of the
worst cases of dry joints in recorded history

I am trying to use a laptop in a car. I have an inverter rated at 50w. It
worked for a few months and then peremptorily stopped with a sudden rattle
from within and no light going on to show that it is ready. When I opened it
up I found a whole power transistor rattling around inside with all three
joints seemingly not connected and the glue from the rear of the transistor
seemingly having come off. Curiously the ends of the connectors don't
actually look as if they were ever connected?? (The holes on them from the
motherboard do look as if at least something was once connected to them as
they are filled with slightly disturbed-looking solder)

Is this just a lousy joint on some cheap chinese-looking inverter which
worked while the pin ends merely touched the mainboard slightly or does the
power charger need SUBSTANTIALLY more than a puny 50 watts to work: The
charger reports that it needs an input of from 100 to 250 volts at 1.5 amps
to give an output of 18.5 volts at 2.7 amps. Can someone do the maths for me
and let me know what power inverter this charger will need please?

I am suspicious of the puny nature of the inverter because although I can't
see a laptop using all that much power, I have also got a huge heavy duty
Coleman PMP400 inverter with fins all over the place and a heavy duty
sounding onboard fan rated at 400 watts (peak surge 800 watts at 3.5 amps)
and after about ten minutes of use, IT starts to overload on this laptop
charger (meaning the red warning light comes on and the inverter starts
giving symptoms of blowing): The red light won't now go off: I am wondering
if I have blown this inverter as well? (Curiously it didnt last as long as
the 50 watt one).