Have you copied your iTunes library over from your old computer, or backup of your library, into your new computer's iTunes library ? If not then you can use an external drive to copy your library over : How to move your iTunes library to a new computer - Apple Support
Or if both computers are connected to the same wifi network and home sharing is enabled on iTunes on both, then you should be able to use that to copy your library over
Or add your library from your backup of your library via File > Add To Library
For the syncing to the new computer, see if this user-tip helps : Syncing to a "New" Computer or replacing a "crashed" Hard Drive
It was written specifically for iPhones but it applies to iPads as well. Some of the steps on that page are slightly different now (it was written for a previous version of iTunes) :
- 5, File > Devices > Transfer Purchases
- 6, Reset Warnings is done via the bottom of the device's Summary tab in iTunes
- 7, File > Devices > Back Up (or Back Up Now on the device's Summary tab)
- 8, File > Devices > Restore From Backup (or Restore Backup on the device's Summary tab)