David Wolfson touched o this point and after reading all the posts, this is a good culprit to your problems. Make sure that the inverter yuo choose is producing a Since Wave. These are generally more expensive but well worth the extra $$.
A Since Wave is the same power that you will get from your household outlests. It's a natural wave produce by the generating plant and all the step and substations there of. it's AC current.
A square wave, or Modified Sine wave may, or may not give you trouble. Most low cost inverters produce a square wave power and really only work well with electric motors and the like. You may get away with it for a while on a laptop power supply, but probably not for long.
A modified sine wave is much like a square wave with an extra step. The inverters generally work with more items, but still do not really produce the proper AC power wave most household electronics need.
Example: My inverter is a 1000/3000 watt rated inverter. Meaning, it produces 1000 watts of continuous sine wave AC power with a surge/peak rating of 3000 watts.
Say I have a microwave oven in my vehicle. the operating wattage for said oven is 500 watts. However, when you first turn it on there's a surge of 1500 watts while the initial eletronics and microwave emitter gets going. Since most microwaves weren't really intended for use in a car, they are built for household power. Household power comes to you from the power company with a Sine Wave. Say your inverter is a modified sine wave. The microwave won't work properly or it will work harder as the wave of the power amplitude isn't quite right. This can cause damage to microwave itself and eventually the appliance will fail.
This is much the same for computer power supplies. My wife's car had a 600/800 watt inverter that we used specifically to power the laptop (An older Dell BTW). I didn't do my research about the Wave process on power and the inverter was a modified sine wave. Well, it worked.... for a while. Pretty soon we started seeing some issues with the laptop and the power supply died. We replaced the power supply and for a month or so, things went great until it started happening again. This time though, the inverter blew an internal fuse. When it did that, it fried the laptop power supply and also took out the power control chips on the laptop motherboard!
That's an expensive fix!
I spoke with a friend of mine who works on ambulances. Fixes them. It turns out that the culprit was the inverter. The one we had, wasn't set up to run household electronics. He showed me a few where some local volunteer groups had replaced one in their ambulance with a cheaper version. It ended up frying all the internal equipment that needed the sine wave to work properly.
So there is a difference in inverters. Sine Wave producing models will give you the best performance and least hassles. Of course they are more expensive.
Hope that helps!