Hi my name is ***** ***** I will be the expert working with you today to help and resolve the problem you have posted.
I am sorry to know that you are facing problem with your Incredimail.
Incredimail is an email client software which you use to configure your existing email in it.
You need to login to the old tower and then you can back up.
Incredimail is an email client it not an email server which you can login and save your emails its like you have MS outlook and you configure your gmail, hotmail or any corporate email address and you get emails in outlook.
I hope I've provided the information you were seeking. Feel free to ask or reply me so that i can continue to help you answer you question further. Thank you.
let me know what email service you are using i can try to get you logged into the web mail and then you can retrieve the emails you want if its saved in the email server.