Since the recovery-mode restore completes and you still get stuck at activation, I don’t think another DFU restore is likely to change anything.
I’d try activation once from a different Wi-Fi network, and once while connected to a Mac or PC running the current Finder/iTunes software. Apple recommends computer activation when activation on the device fails.
If that still gives “Unknown Device,” the important question is whether this is an iPad 2 Wi-Fi model or Wi-Fi + Cellular. A hardware problem on the cellular model can also prevent activation, even though the restore itself completes.
Apple’s activation steps are here:
If you can't activate your iPhone or iPad (Wi-Fi + Cellular) - Apple Support
The iPad 2 is also now listed by Apple as obsolete, so Apple no longer provides hardware service for it. At that point there probably isn’t another software reset or restore procedure beyond what you’ve already tried.