I'm guessing too, but checking the power seems to be a good place to start. If you have a DC voltmeter, and can get access to the right pin on the PS/2 connector of the m10000 (assuming this is possible - I don't have one), try measuring the voltage of the +5V pin with and without the GPS connected to it. I don't know which pin is +5, but a search should find it.
It could be some other interface problem too, like voltage levels or timing on the signals from the GPS; or maybe some sort of conducted or radiated RF noise problem giving the GPS fits. Without the right test equipment, I don't know how you'd go about solving those problems except by and error.
If it works on the roof, I think an interface problem is less likely to be the cause of your troubles.
You've sure to have more signal strength from the satellites on the roof as well as more "visible" to the GPS which might make the difference if the receiver isn't working as well as it should. I'm guessing this might happen if the voltage into the GPS is marginal. But you've also got less possible interference from the RF noise generated by your computers and inverter.
With the GPS on the roof, you've got (I assume) the metal roof to shield the GPS from any RF noise from the other electronics. Did you have the same equipment running when you tried the GPS on the dash connected to the laptop, and when connected to the m10000? If so, I doubt radiated RF is the problem. If you didn't have the same stuff running, try that to see what results you get to help determine the cause. Note that I don't know exactly how susceptible GPS receivers are to RF noise in the first place. But, I read about some boat owners having problems because of a design flaw in a satellite TV receiver that was giving GPS receivers at quite a distance problems (don't remember exactly, but it was quite a ways - on the order of a thousand feet). The latter problem was well documented and not just guesswork because some university people tracked it down and isolated it to the units actually causing the problems.
Hope this helps,