I have a Panasonic G1 and an the ancestor of your TZ10,the TZ5.
If you use the camera in iA(intelligent auto) mode,then it should compensate for low level light situatations by automatically adjusting the aperature and shutter speed.There should also be an exposure adjust button on the rear dial,but I'm certain that this is disabled when using iA mode.l think that if you half press the shutter release then the camera sets itself up for the shot,rather than fully pressing the button and hoping for the best.
If you use the flash,then it will over expose the shot of anything closer than about 6ft and cars on a show stand are highly polished and can reflect flashlight back into the lens,which doesn't help!
I'm sure that there will be others along to give you better advice as there are a few good snappers on here who know what they are doing!