Everything is ok now as I have stumbled back on the old password. But I think I should explain what happened for those who are kind enough to look into my post and have tried to help. And for those who may encounter a similar problem in the future.
About the reset by Apple ID.
I could not do it because I had not enabled the option by checking the check box in the first place. The "You can reset with your apple ID" line in the dialogue box after my false attempts was quite misleading. But it did remind me to take notice of this very useful feature.
Be very careful when both upper and lower cases are used in a password. In my case, 2 upper cases were used when only 1 was intended. It happened when the typing was fast. The worst part is it happened 2 times in a roll and when a password was being setup.
Just hope this answer can be helpful to someone; As we are increasingly burdened with more password setup...