I'm trying to reset my iPad and Apple ID doesn't work

See these support articles:

Restore your iPhone, iPad, or iPod to factory settings [with a computer] - "A factory restore erases the information and settings on your iPhone, iPad, or iPod and installs the latest version of iOS or iPod software."

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

How to erase your iPhone, iPad, or iPod touch

"Learn how to wipe information from your iPhone, iPad, or iPod touch and restore your device to factory settings." Without using a computer. Does not reinstall iOS.

Click here --> How to factory reset your iPhone, iPad, or iPod touch - Apple Support

If neither of the above work, read the "If you can't erase your device" section in the last link, including the last part about contacting Apple.

I own an iPad 2 but I haven't used it in several years. The outdated software makes it very hard to use except for basic functions.

All you said was "doesn't work" which doesn't really help us make a start with being more specific as to solutions and issues. ;-)