Why cant i access my google account on a new phone when I have not factory reset my old phone
You mean that you had to wait 24, and 72 hours to be able to logon again to your google Account. So apparently Google have warn you several times before block your IP (i think).

Concretely, some information is missing in your tracking subject, namely the types of protections you have set up on your Google Account (confirmation email, confirmation SMS, secret key by Google Authentificator, etc).

It also lacks the essential information to know what the exact error message Google is displaying on the screen.

In your security center on your phone connected to your Google Account, do you have any alert related to your problem? This famous Google security center is generally accessible via the phone's settings menu.

In yet another solution, the user has the ability to create special accesses for third-party applications (allow Outlook to access your Gmail account, allow access to your Google account through a Windows Phone).

Maybe you could create a particular access for another type of device, Google will then provide you with an access code, it will want to write it down (without spaces), then enter it as a password to be able to access your Google Account without having you blocked again.

We hope this alternative will help you.