Alright, that's what I was afraid of...
With your iPad still connected, open the "Image Capture" app located in the Applications folder on your laptop.
The Image Capture app should recognize that the iPad is connected and list it as a Device in the left sidebar. It will also show thumbnails of the contents of the iPad’s Camera Roll in its main window.
If it does, you can try importing these photos and then deleting them via Image Capture.
At the bottom center of that main window you’ll see the ‘Import To’ selection field. By default this is set to import to the /Pictures folder under your username. That should be fine.
Click on the tiny button at the bottom left of the Image Capture sidebar. You’ll see a checkbox for ‘Delete after Import’. If you select that it will do as it says and remove all the images from the iPad Camera Roll. It does this as the import progresses.
Then, click Import all.
Once finished, restart the iPad and see if the Photos app is functional again.
If it is, you can sync back any photos you wish to keep on the iPad by importing them from your Pictures folder into iPhoto
(if they are not already present) and then syncing via iTunes.