Cannot sign in. In app store and itunes.

Do you have access to another WiFi network where you can try? That has worked for several people.

Try a restart.

Restart your iPhone, iPad, or iPod touch         

Try a forced restart.

Reset Device.      

If necessary

Hard reset.        

Do a backup and try a factory reset. Then restore from your backup.

Restore to Factory setting.      

Backup - Restore your device from an iCloud or iTunes backup.      

Did you see a message that says 'Your account has been disabled in the App Store and iTunes' https://support.apple.com/en-us/HT208856 "There might be a problem with the payment method that you have on file. When you see the message, don't try to edit any of your account information. Instead, contact Apple Support for help.”

Use the Apple recommended support link above first.

And, if necessary, go here is how to contact iTunes worldwide support via text or

chat using this link https://support.apple.com/choose-country-region/itunes After

choosing your country, see the heading Tell us how we can help.

are you using two-factor authentication? If yes, see:

See Get a verification code and sign in with two-factor authentication https://support.apple.com/en-us/HT204974  Below is an excerpt, but read the whole document. See the bold italics below.

“Whenever you sign in with your Apple ID on a new device or browser, you'll confirm your identity with your password plus a six-digit verification code. There are a few ways you can get a verification code. You can use the code displayed on your trusted device, get a text or phone call, or generate a code from your trusted device [see the additional information in the article].” A trusted device is an iPhone, iPad, or iPod Touch with iOS 9 and later or a Mac with OS X El Capitan and later that you've already signed into using two-factor authentication.

Account Recovery—Two-Factor Authentication (i.e., Recover your Apple ID when you can’t reset your password  https://support.apple.com/en-us/HT204921

“If you can’t sign in, reset your password, or receive verification codes, you can request account recovery to regain access to your account. Account recovery might take a few days or longer, depending on the specific account information you can provide to verify your identity. “After you request account recovery, you'll get an email with a confirmation of your request and the date and time of when you can expect to regain access.” … When the wait period is over, Apple sends you a text or automated phone call with instructions to regain access to your account. Follow the instructions to immediately regain access to your Apple ID.”

There is one more thing Eric Root mentioned that you said you haven't tried. I'll think more about your problem and get back to you if I come up with anything. For now, you can get Apple telephone support  for help in solving your problem using this link https://getsupport.apple.com/?caller=kbase&PGF=PGF63005&category_id=SC0245&symptom_id=23362 Be patient sometimes Apple support is closed to immediate phone support.

contact iTunes Support. See the Apple Support articles below for contact information.   

iTunes Support – world wide 

Apple Support schedule phone call       

What message do you get when you try to sign in and can't?