Macbook password and iCloud password, help!!!

Hi!

I desperately need help! I've been trying to solve this for hours!

Its a bit of a long story and a tad confusing so please bear with me, the situation is, I used to have this very old email of hotmail as my apple ID (the first email), I mostly used it for lodging the iTunes receipts and all of that so it went like that for a long time.

Yesterday I bought a macbook pro and was unaware that during setup it would take the iCloud password and use it as the computer's password as well. So when I tried to change the password to something else, it said to input the iCloud password; I honestly panicked because I couldn't remember it for the life of me, then I went password/verification mail hunting through all of my hotmail accounts and unluckily for me I don't know what happened or what I did wrong that once I managed to open them, all of my mails were gone on those accounts. Then I horribly decided to ditch said accounts (the first email and another hotmail that I have) and change the main mail of my apple ID to a gmail account. I did so without any problems. I could change the apple ID in all of my devices, including an iMac.

My biggest problem now is the macbook pro, that whenever I want to log out of iCloud/change the password or make any change in general it asks me for iCloud's password, which it seems its the original password of the apple Id (with the first email) that I couldn't find and that now the mail is changed(to the gmail account) and won't accept the current iCloud's password, and whenever I try to recover the password or change it with the first mail address I get an email saying that its indeed been changed.

I've tried with tutorials online that says how to change the apple Id but I can't make changes without the computer's password( the same of iCloud), whats makes it worse my old email address still appears as the apple Id xxxxxxxxx@hotmail, instead of xxxxxx@gmail. Strangely enough it seems to have taken some of the changes because the information of the account appears and the current password can be changed from the security and privacy settings. And I've also opened iTunes and Face time with the new apple iD account and password without any problems.

But now I can't make any changes without the password!! It doesn't accept the new one, no matter how many times I try to change it.

And can't log out without the password that I don't have therefore can't "officially" change the apple ID or iCloud on the computer, its like a vicious cycle!. I'm really afraid that if I turn off the computer I won't be able to open it again.

Ahh I'm sorry if its confusing, english is not my first language and its hard to explain even in spanish.

Please if anyone can help I'd be so grateful.

My other option is resetting the computer to factory defaults, since its new and haven't dowloaded or installed a lot of stuff yet. But I don't know how to.