800x480 is the ideal for the Lilliput, and it's also a 16:9 widescreen resolution. It's very likely that your laptop can output that.
You might also try other, higher resolutions. They may work as well.
You don't have a docking station. You have a port replicator. There is a huge difference.2) Remote power on: Initially I purchased the docking station so that I could wire an external power button to the docking staions power as was done by some members here. The problem with this is that the docking stations power button has absolutely no effect on the laptops power. I'd hate to have to open the laptop to tap into it's own power button or even connect more cables to it for a wake-on-lan option. It would defeat the whole purpose of having an easy-disconnect docking station.
A docking station typically has its own power supply that will power a laptop, as well as charge it.
Another forum member made an auto-on module for laptops. I know nothing about it, as I'm not using a laptop on my system, but I'd think it would be worth investigating.
There are other options for powering on the laptop remotely, as well.
See my answer for #2 above.3) Standby: Initially I was planning on using the laptops standby option. I can wake it by pressing any key on the laptops keyboard. I was hoping I could also wake it with the powermate since the docking station provides for a couple of "always on" USB ports. Two problems with this:
a) The USB ports would not be "always on" when installed in the car because I think I should cut power to the docking station when the car shuts off so as to avoid battery drainage. I want to install a USB keyboard eventually too, but this would probably also not work.
b) The powermate doesn't work even with power still going to the DS - or even when it's plugged directly into the laptop. Are there any other ways to wake it by connecting something to the DS?
The unit I mentioned has a startup/shutdown controller that is triggered by the ignition.