"For instance, my old iPod will no longer turn on." Not turning on has nothing to do with credentials or phone numbers.
See How to reset your iPhone https://www.digitaltrends.com/mobile/how-to-reset-iphone/
If this does not work and an Apple Store is open in your area, then you can go there to deal with this problem. In this case, you can make a genius-bar appointment (https://www.apple.com/retail/geniusbar/) if you want.
If you have a problem account other than the one on your iPod (or the one on your iPhone after reset or repair),
See: If you forgot your Apple ID https://support.apple.com/en-us/HT201354 and
If you forgot your Apple ID password https://support.apple.com/en-us/HT201487
You also can use Having trouble signing in/iForgot https://iforgot.apple.com/password/verify/appleid
And you undoubtedly will need to see If you forgot the answers to your Apple ID security questions https://support.apple.com/en-us/HT201485
Before trying to answer your security questions is very important that you think about your questions and their answers carefully and try to recall all details you can. If you don't answer them correctly enough, then you easily can lose control of your account.