If you have an Internet account, open the email reader you use for sending and viewing email. Try to figure out where the SMTP server (for outgoing mail) and the POP or IMAP server (for incoming mail) are configured.
If you're feeling really adventurous, ask a close friend if you can configure an email reader on the friend's computer to check your email account. Some email readers support multiple email accounts. Or, you might be able to configure a built-in email reader that your friend isn't currently using.
By the Way
You might find that you can check your mail from your friend's ISP network but you can't send outgoing mail from your friend's network to the SMTP server on your own ISP's network. Many ISPs do not allow external email messages to bounce off their SMTP server.
If you try this exercise, it is also important to remember that, although reading email is independent of the task of establishing an Internet connection, most email readers offer the option of automatically establishing a connection when you check your mail. You'll need to make sure you're connected to the Internet when you try this experiment.