If you are signed into the same Apple account on your computer as you are on the iPad, and if the songs show up in your iTunes library and you have selected them all to sync ... I am at a loss.
Try two more things.
Check in the Summary Tab of iTunes (when the iPad is connected to the PC and iTunes is running and after you have clicked on the iPad name) - and make sure that you do NOT have the iPad set for Manually Manage Music and Videos. Make sure that that option is unchecked. If it was checked by some chance, that could be the reason that the songs will not sync.
Finally, quit everything, restart everything and try again. Quit iTunes, reboot your PC and rest the iPad and then try to sync again.
Restart the iPad by holding down on the sleep button until the red slider appears and then slide to shut off. To power up hold the sleep button until the Apple logo appears and let go of the button.