I can't log into my computer with the password I have been using

Reset your Mac login password…

https://support.apple.com/guide/mac-help/reset-your-mac-login-password-mh35902/mac

I've tried to log on to iCloud through my computer Mac mini 2014 Version 10.15.3 without any success. Will not accept my ID or password. When I go to iCloud.com, it works. Shouldn't I be able to do this through my Mac?

Yes it should, try this...

To find out if it's system wide or user specific, try this...

Open System Preferences>Users & Groups, unlock the lock, click on the little plus icon, make a new admin account, log out & into the new account.

Does it work in the new account?

Were you successful?