How do I unlock my iPhone 4s without Apple Account or password?

Apple ID and Activation Lock

iCloud uses Apple ID credentials.

If you do not remember the Apple ID Password then follow the steps given in this Apple Article -> If you forgot your Apple ID password - Apple Support

If you do not remember the Apple ID then follow the steps given in this Apple Article -> If you forgot your Apple ID - Apple Support

If you are the owner or the owner has shared all information with you then to open Activation Lock:- If it is Activation locked, read here --> Turn off Activation Lock - Apple Support Activation Lock for iPhone, iPad, and iPod touch - Apple Support

Learn how to remove a device from a previous owner's account.

If you are not the owner and do not have the Apple ID and Password then there is no way that you can get into this iPhone unless the original owner shares the Apple ID and password with you. If you are lucky you can get into this iPhone if they (owner) accidentally remove the device from their Apple ID.

To start with, you probably didn't fully reset it. To do that you do what is in here --> What to do before you sell, give away, or trade in your iPhone or iPad - Apple Support

It depends upon what exactly is displaying on the screen. If you see a "Locked To Owner" message, one referring to iCloud locked, or activation locked, read this article about removing Activation Lock --> How to remove Activation Lock - Apple Support Unless you have the account information that set the lock, or the original receipt from Apple or an Apple approved vendor, or can demonstrate legal inheritance from a deceased owner, you cannot remove the lock; recycle the device.

If it is simply asking you for her account information, enter that information. If you do not know it, ask her. You can try resetting the information but since you are now essentially in the same position a thief or hacker would be in trying to get into a stolen iPhone you probably won't be able to. This article tells you the various ways you can try to discover your forgotten Apple ID --> If you forgot your Apple Account primary email address or phone number - Apple Support Typically an Apple ID is an email address you have used. If you are currently using a mobile device that is logged into your account, go to Settings and tap your name at the top. Look in Keychain, and in a browser's security settings if you use it to automatically sign into Apple when using a browser. This article outlines what to do If you forgot your Apple ID password --> If you forgot your Apple Account password - Apple Support

or go directly to this link --> http://iforgot.apple.com/

If you find you can’t sign in, reset your password, or receive verification codes, you can request account recovery (read this support article: How to use account recovery when you can’t reset your Apple Account password - Apple Support ) to regain access to your account. Account recovery might take a few days or longer, depending on the specific account information you can provide to verify your grandmother's identity. More detail in —> Activation Lockout Issues - Apple Community

If you still need help this page provides country-specific Apple Support contact information ➞ Contact Apple for support and service - Apple Support