I performed an Export to X3D on the attached blend file consisting of the default cube with an image texture. The image was added to the blend file by going to the UV image editor and opening an image from the textures subdirectory 'textures\vts.jpg' . The image was then packed into the blend file. I then selected the default cube and added a texture to it. I set the type to "Image or Movie" and for the Image I selected the image that was packed in the blend file. The ImageMovie file name was displayed as "//textures\vts.jpg" . When I performed the Export to X3D the TextureImage url field was empty.

<ImageTexture DEF="vts_jpg" url=" " />

It should have been set to a value that includes the relative path of the image packed in the blend file.

<ImageTexture DEF="vts_jpg" url=' "textures/vts.jpg" ' />

Also note that the url field in X3D is of type MFString which is an array of Strings since it can contain more than image file name. Therefore there really should be an extra set of single quotes outside of the double quotes for the texture file. If you had multiple texture files in the url field, then it would look something like this

<ImageTexture DEF="vts_jpg" url=' "textures/vts.jpg" "textures/file2.jpg" "textures/file3.jpg" ' />

The X3D player will try to load the first one in the list, and if it fails to load it will then try the second file listed and so forth.

I am using blender version 2.56.0 r34154 on a windows XP machine. Attached is the blend file to reproduce the problem and the X3D file with the expected output.