Most of the ISPs normally shutdown the inbound SMTP traffic from out-side of their internal network sicne SMTP is not a secure protocol and is liable to too many security issues.
If you face this problem, you can set up your POP3/IMAP server to your old ISP's, for SMTP you have to use the one your current ISP provides you.
It means the POP3 and SMTP services are provided by different ISPs.
Some free ISPs may not publish their SMTP servers' address so it's hard to access your old email accounts if these mailboxes are located in other ISPs.
Another walkaround is to use Yahoo! Mail or Hotmail's external mail feature to access your old mailboxes.