New computer

I suggest that for the time being you connect the computer directly to the router or modem via an ethernet cable in order to avoid confusion between wireless security password and e-mail password.

Presumably when you first signed up for the e-mail account you wrote down the e-mail account user name and password and put is somewhere safe. If not you may have been asked some security questions by the provider in case you forgot the password. Try to sign in now and there may be an option to retrieve password if you can answer the security questions (usually mother's maiden name, name of first pet etc).

if the above does not work you probably have a network password. IF the network has an encrypted setup you can correct it by posting the type of router you have. Routers usually ahve a fixed IP address for the router settings and the password can often be retreived or changed from here. (IP varies by cmpany but someone may be able to tell you what that ip is).