Videos taken on the iPhone will not sync to the iPad
The fact that iTunes silently skipped informing you that it did not add the videos is most probably caused because you checked the "Do not show this message again" upon the prompt the first time. 

Are the videos in MOV or MP4 format? You can try installing the free VLC app on your iPad  and then add any video files to that app via iTunes File Sharing. Simply:


Run iTunes and connect the iPad
Enter the iPad settings in iTunes and navigate to the "Apps" tab
Select the VLC app under "File Sharing" (scroll all the way to the bottom to see "File Sharing")
Click on "Add files..." and select the videos from your PC
Click on the iTunes "Apply" button.


This should add the videos to the VLC app on your iPad from where you can access and play them.