http://starmade.freshdesk.com/
help.star-made.org
the link changes. They are both the same site though. There is a option there to open a new ticket. Get logged in there and try that out. I will keep looking. For a few more minutes.
I am seriously thinking that your computer doesn't support openGL There are two major thingymajigs for turning all the fancy code into graphics and such. One is DirectX, which works well enough. Though it is extremely OS dependant. Like windows only extreme. OpenGL isn't the best and from I have heard needs some major revising. It still works with pretty much everything under the sun though.
Starmade uses OpenGL. There is no directX option that I know of for this one. The error you were getting is one given a lot when OpenGL isn't hardware supported by the system.
I am still not sure though on this one. If you have a slim case it may be hard to upgrade your power supply and put a graphics card in there. Though it could be doable. I haven't really dealt with slim cases much. I wouldn't try doing that if I didn't know what I was doing. Get someone you know is good with computers to take a look at this if you know anyone.
Edit:
Is there any chance this is what your computer looks like?
http://www.amazon.com/Gateway-SX2865-UR348-Desktop-Pentium-Processor/dp/B00CHYKVR4