If you are interested in pursuing it, can you please provide more information as below?
Sorry for all the questions, but wanted to make sure I provide the right suggestion for your situation.
Otherwise, you may also want to discuss more with ASUS support to clarify why shipping is not covered in this case.
1. Where did you buy the notebook from and what is the purchase date?
2. Which notebook model was it and did you buy it new or refurbished?
3. Which version of Windows are you using and have you connected to the internet to activate Windows? Please provide more details about any error messages if possible.
4. Are you still using the ASUS Windows image or did you install your own Windows image (or upgrade Windows?)? If you check Windows System Properties, check for the ASUS logo as in the screenshot below from my G750JZ unit to confirm you are still using the ASUS Windows image.
If it's not too much trouble, try to include a screenshot from your unit using the 'printscreen' key and pasting the image to Microsoft Paint to save.
Thanks.