I personally would scrounce for second hand flourescent lighting ballasts. I bet you could find some on the cheap if you look at those building material recycle stores. Contractors frequently will dump their spare commercial lighting materials at these places, and it shouldn't be hard to find some florescents with ballasts.
Sandwich the poster between two sheets of glass or plexi, build a box around it, and put florescents inside, you should have a poster light box. Oh, there was a good point made from BobA's link. Since florescents put out UV light, it is best to get glass or plexi with UV filtering to best preserve the poster, or put a UV blocking window tint on it. I didn't think about that one before.