I can't access my iCloud account using my username and password

Your Apple ID say example1@gmail.com is signed in the device .

Maximum limit for creating Apple ID from the hardware address of iphone is three , you can't create more Apple ID accounts , however again sign in with your same Apple ID and it's account credentials ( in fact you have signed out the Apple ID ) in the empty fields or sign in with another apple id that was created from another Mac / iPad or different iPhone .

See the article 

Sign in with your Apple ID - Apple Support

Note : if you are trying to create email account already used from this iPhone say example2@icloud.com this as an Apple ID and maximum limit of creating this mail address has been reused , the account will not be created.

You can use a different Apple ID already created from a different browser and then add the mail account Add an email account to your iPhone, iPad, or iPod touch - Apple Support

Either the mail address or password that you are trying to sign in is incorrect as there might be typing mistakes in both , enter the mail address and password correctly , sometimes if incorrect credentials are entered multiple times server assumes some one is tricking and using phishy attempts .

Server doesn't know who is using the Mac , it assumes and locks the account see the complete details in the article If your Apple ID is locked or disabled - Apple Support

The second reason if Apple ID account doesn't exist on the iCloud and it is erased from the server How to delete your Apple ID account - Apple Support

And that can be verified using this link https://iforgot.apple.com/appleid#!§ion=appleid

Enter the correct credentials if the account exists a green check mark will always appear the account is verified .

See Apple ID – Official Apple Support

Note : if Apple ID is locked from server , revealing account credentials to apple support advisors , the account can be opened .

( a ) If you lose answers for Apple ID provide credit card details that was added in the account .

( b ) if you have lost Apple ID password provide invoice copy of Mac to apple support advisors .

( c ) Contact apple support , they will send a link on mail account , click on link after 24 hours to reset apple id password , however the link is valid for additional 3 hours .

( d ) Support pin is used by apple support advisors to verify the account when you know apple id password Generate a temporary Support PIN - Apple Support

wisper77 wrote:

Ok have been having this happen for a minute now. My username and password don't work on phone or ipad. Keeps telling me they are wrong. I know they are not. It will not let me login to my account on either device. When I try to connect to iCloud through a browser I get "iCloud encountered an error while trying to connect to the server."

Clearly, I know my username and password as I am using the same account to post this. As it stands, I cannot access any of my purchased apps, which means I cannot do my job, as some of those apps are for my job.

Seems there was an issue earlier but has been resolved Apple - Support - System Status

See the article If you can't connect or sign in to iCloud - Apple Support

If you still need help

If you still need help signing in to iCloud, update your iPhone, iPad and iPod touch to the latest version of iOS or iPadOS, and your Mac to the latest version of macOS. See the iCloud system requirements for more information.

Your Apple ID should not be locked from server , also see this article If you see a Could Not Create Apple ID or Could Not Set Up iCloud message - Apple Support