HELP: Getting good photos of props in a museum

I went to the Where Science Meets Imagination exhibit this past weekend in Wichita, KS. I tooks lots of pictures, but was disappointed in many of them. I was trying to get close up shots of greeblies on the models.

The lighting on some of them is extremly poor. You are allowed to use flash, but you run into reflection problems. I have a lower end camera (~$100 Sony). It works great for me and most of the time gets the job done. My philosophy turned to snapping as many as I could take in hopes that some would come out good. The strategy worked good, except for some where the exact shot that I need was blurry every time. It looked okay on my camera display, but was blurred beyond use on the computer.

Now, I have a couple of problems. The probe droid for example. It's legs are almost totally in the dark. I took a small flash light and shined on them...it helped some I was nervous I would be busted by a power hungry museum employee.

I am planning on going back before the exhibit leaves at the end of the weekend. Does anyone have any advice for taking close up reference photos behind glass in poor lighting with a cheap camera?