How can I remove color cast created by a defective scanner?

Not sure if this is the best practice, but it gets rid of the cyan background.

1. Open the image in Photoshop
2. Duplicate the layer (so you'll have a backup)
3. Go to `Image -> Adjustments -> Replace Color...
4. Set the Fuzziness to ±15.

5. With the Add to sample color picker (the one with the + sign) sample the color at different locations in the background such that you only get the background color in your selection, not the face:
   

6. In the Replacement part of the window change the Lightness to +100. This will replace the selected color range with white.
   

7. Additionally you can play with the Fuzziness slider to remove the blue cast from the face as well.

8. Hit OK in the Replace Color window.

Result:

That is not a colour cast. A colour cast is an overall tint or bias toward a certain colour. This can be fixed by pushing the colour balance the other way. The image you posted is simply missing the red channel entirely. Regular techniques to shift the colour balance wont work as there is no red* to boost

This cannot be fixed unless you fill in the missing data somehow.

* my initial diagnosis of missing red channel was based on the cyan background, cyan is 0% red, 100% green 100% blue, which is exactly what you get when you start with a white (100/100/100) background and drop (zero) the red values. However upon examination, there is data in the red channel but it's corrupt / not what you would expect to find.

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Ok, so what can you do? Images of faces have very little blue data, so the only good data we have is the green channel by itself, which is effectively a greyscale image.

A skilled photoshop artist could recolour a greyscale image, but that's a complex process. The only thing that can be done simply is apply a skin colour to the whole image.

Another option is to attempt to rebuild the red channel somehow. Here I've rebuilt the red channel using the channel mixer using 60% of the original red channel and adding 60% of the green channel.

Given the aforementioned lack of colour information in the other channels this is really akin to applying a single colour to a greyscale image (though it does preserve a small amount of information from the otherwise defunct red channel). Using curves to blacken the hair a bit and reducing saturation yeilds this result, which is about as good as you will get without manually masking and recolouring each area!