having first hand experience on the early model highlanders i can tell you you will NOT be able to power up a PC with the cigarette lighter. I've seen highlanders that would blow a fuse using a portable gps system. If you MUST go inverter i would definitely suggest you connecting it to the battery with a fused heavy gauge wire.
Even if you do install it properly you will probably have battery issues a short while after installation with a system running at 300 watts. That is, unless you like the idea of having to shut down the pc AND the inverter each time you turn your vehicle off.