I have several different ideas about how you can get books for you students.
Have you heard of the freecycle movement. If you go to freecycle.org it will take you to the list of many in our area. KC Freecycle is the biggest and best one that there is. I am sure that if you posted your story, you would get several responses. I would clearly post what cities you would be willing to travel to to pick up books.
Also, now that Garage sale season is in full swing, take advantage there. If you tell the people your situation, they may likely throw them in for free or greatly reduce the costs.
I also believe that the Lansing city public library was started with donations from another libraries book sale. I know that Olathe is having their Spring book sale for the public soon. You may be able to contact them and see if they would donate the books that did not sell to your school.
There is also the Scholastic book warehouse sale that offers books cheaply. Does Scholastic know of your situation? It seems that they would be willing to donate some books.
Also, I would contact local business for cash donation to get a library started.
Have you thought about writing a grant? I would think that a quick internet search would lead you to several sites of people trying to promote literacy.
Hope this helps!