Ah, welcome to the world of Blender traps!
Have you tried textured view? To the right of to the menu where you switch between Object Mode and Edit Mode (and some more), you find one that shows sort of a globe in wireframe mode, a white ball when you are in solid mode, a white cross on a red circle when you are in textured mode and a somewhat coloured ball in rendered mode.
You need textured mode. Rendered mode would be ok, too, but it is a bit slow and you need to play with the lights first. You are likely to sit in darkness or misinterpret what you see because of the lighting.
If you are in textured view, and you don't see the textures on the model, you need to assign the texture image to the object, for Blender only:
Show "UV/Image Editor" in one panel/area/viewport.
Go to Edit mode (press TAB), select all (press a once or twice until all is highlighted). You will see the UV map in the UV editor, but no image.
If this is the case, click on the icon besides the Image menu (to the left of the + and New button). You should find the texture already listed and just need to select it.
If the list is empty, select Open Image in the Image menu and open the image. It will then automatically be assigned to the current object. You may need to re-assign it to other objects, but just performing the steps above. I.e., you open it only once.
Hope that helps.