You most probably could replace the screen if you can find a replacement for it.
Here is a link to the Ifixit guide to repair a Vtech Mobigo Touch which should be close enough to your model to allow you to open it to gain access to the screen.
Hopefully on the back of the screen itself there will be stamped a part number and by searching online using this number you may be able to locate a supplier for the screen.
VTech MobiGo Touch Learning System Repair
This has to be weighed up against the fact that you can get one on Ebay for between $US40-70 This is just one example. You may be able to sell yours as faulty - good for parts to try and recoup some of the cost of getting another one.