As described, your iPad battery may have reached the end of its usable life. If the battery has failed, the iPad will not successfully boot to a running state and will boot-loop - even when connected to its Power Adapter:
iPad Repair & Service - Apple Support
These support pages should help with troubleshooting battery and charging issues:
Charge and monitor the iPad battery - Apple Support
If your iPad won't charge – Apple Support
Troubleshooting generally requires substitution of the Power Adapter and cable for another known-good item. Most models of iPad require a Power Adapter rated at 12W or greater to reliably charge. 5W Power Adapters intended for older models of iPhone are inadequate to charge an iPad; if the iPad charges at all, charging will be very slow.
Be aware that many computer USB ports cannot source sufficient power to charge an iPad. Unless explicitly designed for charging connected devices, computer USB ports are typically limited to 0.5-1A @5V (i.e., 2.5-5.0W).
If you continue to experience difficulties when using an appropriate Power Adapter of 12W or greater, you might be best advised to seek assistance directly from from Apple Support. You can contact the Support Team using the Support link at top-right or bottom-left of this page. Alternatively, if you have access to another Apple device, you can initiate and manage your support cases using the excellent Apple Support App. If not already installed on your iPad, the App can be downloaded from the App Store:
https://apps.apple.com/app/apple-support/id1130498044
You might also visit the Genius Bar at your local Apple Store or Apple Authorised Service Provider (AASP) - where the technicians will be able to test and assess your iPad, Power Adapter and cable(s):
Genius Bar Reservation and Apple Support Options - Apple
As for troubleshooting error #4013, you’ll find guidance here:
If you see error 9, 4005, 4013, or 4014 when you restore your iPhone, iPad, or iPod touch - Apple Support
If you continue to experience difficulties, you might be well advised to seek assistance from Apple Support or the technicians at an Apple Sore or AASP as described above.