I'm rather lost but I'll try to point you in the right direction.
When you change ISPs you normally lose your old email account with your former ISP, so I'm unsurprised if you can't get access to it.
It's normal for any email account to ask for your password unless you've your email client (if you're using one) to submit it automatically. We'd need to know which email client you're using (if any) to tell you how to set that up. (By 'email client' I'm referring to a program specifically used for access your emails, such as Outlook Express, Thunderbird or Windows Live Mail. If you're using webmail instead, where you access your email through your web browser, please let us know).
However it's rather daft to use any ISP-based email system anyway (precisely because you'll lose it when you change ISPs). It makes far more sense to use a third-party email service, such as the excellent one offered by GMX:
http://www.gmx.co.uk/