On the basis of your description, your iPad battery appears to be failing - and given the age of your iPad, it is very likely that the battery has reached the end of its service life.
Your iPad battery may still be adequate to support use whilst connected to a Power Adapter (charger) or an external Power Bank, but not when connected to a computer via USB. Many USB connections on PC/Mac computers cannot supply sufficient power to charge/run a connected iPad.
If the computer must power the iPad during the restore process, you will need to identify a USB port that can provide at least 10-12W (~2.4A) power. Unless your PC/Mac is relatively modern - and has a USB port explicitly designed for external device charging, this may be difficult to achieve.
On the basis of the device tags appended to your post and your description, you have an iPad4 - potentially running iOS 10.3.3 (WiFi Only models) or iOS 10.3.4 (WiFi & Cellular).
If the iPad battery needs replacement, both cost and limited ongoing utility of your iPad will likely make this an uneconomic proposition. Apple do not themselves offer a repair or battery replacement service for iPad - and the chargeable exchange programme, sometimes offered in lieu of battery replacement, may not be available for the very old iPad4.
Update support for iPad4 ended September 2017. The final iOS releases for this model were iOS 10.3.3 (WiFi Only models) and iOS 10.3.4 (WiFi & Cellular). iPad4 cannot be updated to any later major version of iOS as it lacks the minimum hardware requirements needed to run more recent versions.
Many App Developers have also dropped support for older devices and iOS versions preceding iOS11/12/13 - and have withdrawn older versions of their Apps from the Apple App Store. Withdrawal of Apps supporting older models of iPad is making their utility and usefulness significantly more limited. Once compatible versions Apps are withdrawn, you’ll not be able (re)download or (re)install them - as may be necessary following a potential battery replacement.
If Apps that you need to use now have higher minimum iOS-version requirements, your only option is to replace your iPad with newer model.
I hope this information is helpful - if only in clearly stating your current options.