IPAD 2 Stuck in restore mode

Presumably your iPad indicates that it must be restored:

If you see the Restore screen on your iPhone, iPad, or iPod touch - Apple Support

These support pages outline the available methods to restore an iPad - either from a backup, or to Factory Settings:

Restore your iPhone, iPad or iPod touch from a backup – Apple Support

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

Restore all content to iPad from a backup - Apple Support

You’ll need access to either a Windows PC (with iTunes for Windows installed) or a Mac (with iTunes or Finder - as appropriate for the installed version of macOS).

Download and use iTunes for Windows – Apple Support

Update to the latest version of iTunes – Apple Support

Use of a PC or Mac computer is unavoidable. If you don’t have access to a suitable computer of your own, that of a helpful friend or family member will suffice. Alternatively, the technicians at the Genius Bar of your local Apple Store or Apple Authorised Service Provider (AASP) will be delighted to assist.

Genius Bar Reservation and Apple Support Options - Apple

You need to be aware that very old first generation iPad2 can only be updated to iOS 9.3.5 (WiFi Only models) or iOS 9.3.6 (WiFi & Cellular models).

Apple ended update support for iPad2 in September 2016. Your iPad cannot be updated to iOS 10 or later major versions of iOS as the internal hardware does not meet the minimum technical requirements for new versions of iOS/iPadOS. This limitation cannot be bypassed; iPad2 is a 32-bit architecture device, whilst all recent versions of iOS/iPadOS are designed for 64-bit hardware platforms. iPad2 is obsolete.

Compatible Apps for your iPad are no longer available - as third-party developers have dropped support for 32-bit devices and many for iOS versions preceding iOS11/12/13. As older versions of Apps are removed from the Apple App Store, you’ll not be able to (re)download or install them - which may severely limit the usefulness and utility of your iPad. As such, if you want or need to access most current Apps, requiring more recent versions of iOS, you’ll need to consider replacement of your iPad with a newer or current model.

Of current models, even the entry-level iPad9 has specifications and capabilities that will massively outperform you current iPad - and is compatible with the vast majority of current Apps. Other models are more powerful still.