Change Apple ID Password Failure

I lost a device so I need to change my Apple ID password only but not my Apple ID(email). How do I do this successfully? After investing a lot of hours following on line community tips & tricks, I still have to login to iCloud using my same old PW.

I have been trying for a week to get my MacBook Pro (OS X Yosemite, Version 10.10.3) and iPhone (IOS 8.3) to recognize my updated PW (now on new PW#3). I even changed the # of characters in the PW each time. I can not trick iCloud into recognizing a new password. However, when I check my account the PW length is changed to the # of characters to my newest PW#3. Crazy! On my Mac I deleted my old cloud account (settings/icloud/delete account) as recommended. Then I tried signing back in with my same Apple ID/new PW#3. Nope. Not working. I tried waiting a few days for the system to reboot and the stars to realign (praying meanwhile). Nope new PW doesn't work. With version #2 of my new PW, the system rejected it as a new PW because I had used it in the last year even though the system never recognized that as a PW either. I am freaking. My new mini iPad delivers today. I want to set it up using new PW #3. The nerd pros (said with affection) keep telling users to be more security conscious and change our PWs often. This is why we do not follow their advice, because we can not.

I need a roadmap on how to make the system forget my old PW and accept my new PW. Apparently, I am not alone based on the number of posted comments on this topic.