Restoring iPad 2 without Wi-Fi connection

You should be able to restore it using a computer

You can try a clean install of your device after a factory reset:

First make sure you have a backup

How to back up your iPhone, iPad, and iPod touch - Apple Support

Then facory reset your device:

Restore your iPhone, iPad, or iPod to factory settings - Apple Support

And set it up without a backup. See if the issue persists.

If it still does not work it is a hardware issue unfortunatly I don't think there is any service avaiable for your iPad 2 as it is discontinued

If that solved it there was a software issue. Try restoring the backup and see if it still works.

if that made the problem come back the backup is the problem

Good luck!

The iPad2 is obsolete. Restoring the iPad will completely reset the iPad, losing all locally stored data and non-default Apps that are already installed.

Be aware that all compatible 32-bit Apps have been retired and removed from the Apple App Store - and as such you'll not be able to download or reinstall any third-party Apps to your iPad2. While you should be able to restore the iPad using a Windows PC with iTunes for Windows installed, or a Mac computer, the iPad will have limited usefulness.

If you are unable to connect to WiFi, start with a restart of your WiFi Router - as this can sometimes clear an issue when the correct WiFi Password is being used, but is rejected. To restart your router, disconnect power from the router for at least 30 seconds - then reconnect power to restart. After your router reboots (which may take several minutes), force restart your iPad:

Force restart iPad (models with the Home button)

Press and hold the top button and the Home button at the same time. When the Apple logo appears, release both buttons.

If the problem is not resolved with a restart, you'll need to perform basic WiFi troubleshooting - as detailed here:

If your iPhone, iPad, or iPod touch won’t connect to a Wi-Fi network - Apple Support

Recommended settings for Wi-Fi routers and access points - Apple Support

Consider that your Router, to which you are attempting to connect, may be configured to require support for security features that are not supported by older versions of iOS. If you have an older iPad and your router is configured for WPA3 or WPA3/WPA2 mixed authentication, you will need to change this to WPA2 PSK(AES). Newer models of iPad support WPA3.