If I do wind up getting a new device. How can I get my photos and apps without synching to my old iPad 2? I am afraid of synching with it since it is corrupted. I have not backed up to iTunes in years. But since both devices are corrupted, don't see how that would help. Hate to lose everything. But looks like that could happen.
If you do not want to restore from a backup you will need to save all your photos and other non-Apple purchases off the iPad to another device, computer, or online.
If you don't have too many photos, you could try using the Shared Photo Stream feature for iCloud. It's a bit too cumbersome to transfer thousands of photos, a couple hundred shouldn't take more than 30 minute or so of organizing.
The Shared Photo Stream albums (not Photos Stream) are permanent, and will sync to any iOS device you enable them on; as long as they use the same Apple ID. Despite the name, you are not required to actually share them.
Flickr is another possibility. Again, time consuming.
DropBox, Google Drive, etc. There are dozens of online storage services you can use, depending on how many pictures you need to store.
Or you can copy them to your computer. If you are using Windows, the iPad should mount as a USB drive. You photos will be in the DCIM folder. On a Mac, you can use the Image Capture app.
Don't forget to save documents from other apps. Go thorough all your apps to make sure you don't miss any. Most will have, as a minimum, the ability to email documents.