How do you know "No way in heck that takes 140watts rms of power" ???
The problem is most likely because of startup surge. Your computer may not take 140W of power when fully running, but it may easily exceed this when first turned on for the first few 10's of milliseconds until the input caps charge up. Enough for the protection circuitry of your inverter to kick in and shut down.
Unplug your inverter, plug in your computer, turn on your computer, then turn on your inverter. The power ramp will be slower and you'll most likely power up successfully.