If you do in fact have an iPad2 and have never had its battery changed, the iPad's battery is very likely to have failed due to age. Even when connected to its Power Adapter, an iPad with a failed/dead battery will not boot to a running state.
The iPad2 is very old and long-ago obsolete model. Apple no longer offer repairs or battery replacement for the iPad2 or other obsolete models of similar age.
For information, Apple ended update support for the iPad2 in September 2016. You need to be aware that your iPad2 cannot be updated to iOS 10 or later major versions of iOS, as the internal hardware does not meet the minimum technical requirements for newer versions of iOS/iPadOS. Your iPad has a 32-bit system architecture, whilst all recent versions of iOS/iPadOS are designed for 64-bit hardware platforms.
You also need to consider that compatible Apps for older models of iPad are no longer available - as App Developers have dropped all support for 32-bit devices. As older versions of Apps supporting 32-bit devices have been 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. Should you manage to restore your iPad using your Mac, the only Apps that will remain on your iPad will be those included with iOS - many of which may themselves no longer be usable.
If you iPad is not recognised when connected to your computer, try using a different USB port; if your computer has both USB-C and USB Type-A ports, try using the USB Type-A port of the computer. If difficulties persist, this support page may help with troubleshooting connection issues:
If your computer doesn't recognize your iPhone or iPad - Apple Support