Ok here is the box you need to change. I think you got it wrong way round when you explain your issue too. You went from material to solid mode ... not the other way round I guess.
Basically, what's happening here is that. The solid mode is an opengl operation so it uses a different color operation for showing color on screen. Where material mode takes the material color into consideration. Solid mode are usually usually a quick way to set up simple color to work on the models before heading onto material creation.
And here is the same file with the colors changed!