If you are trying to activate Vegas Pro on your new computer, you will need to use the email address and password that you used to first purchase/register/activate Vegas Pro at the time of its purchase.
If you have tried activating Vegas Pro using the email address that was originally used to purchase/register/activate Vegas Pro and whatever password is associated with your MAGIX My Accouint linked to that original email address and activation does not work, you will need to contact Vegas Support via the Contact Support link at the bottom of the following Support webpage - https://www.vegascreativesoftware.info/us/support/vegas-pro--1/
In contacting Support, it would help the Support team a lot if you provided details about your Vegas Pro such as the version, date of purchase, its serial number, the email address that you used to purchase/register/activate Vegas Pro, the purchase order number (if available).
I'm not sure why there was a need to change your MAGIX My Account password just because of having a new computer. Your original MAGIX My Account email address and password should have worked fine on any computer. Certainly, I've never needed to change my MAGIX My account password on the many times I've got a new computer.
The activation process is to open Vegas Pro and it will lead you through the activation process on a new computer by first asking you for your MAGIX My Account details (i.e. email address and password). After linking to your account, the activation process will then ask you to enter your Vegas Pro serial number and the original email address again, and then it will continue the activation process which includes asking you to hit an OK button on two occasions I think it is.