Just a user tip here, I'm not anybody official.
To run dxdiag, just hit Win-R, (or press Start button and then "Run") and type in "dxdiag", then press enter.
See what version of DirectX you have. It sounds like maybe you don't have Directx 9.0c installed?
If that's all good, then try DL'ing a newer driver for your video card. If you use an Nvidia card, you can grab new drivers very quickly and painlessly from
www.nvidia.com
And you're not the first person to find the demo less temperamental than the full game!
Also, if you read this before a Slitherine guy replies, go ahead and post your OS, video card, etc. They're going to ask for that info before proposing any solutions beyond what I've offered above.
Above all, hang in there! You're almost into the best game you've played in years. Legion Arena rawks, and the community is small but very high-quality.
edit
hah! Pip replied while I was typing!