I am going to change my internet connection from at&t to buckeye cable will I lose my email account or can I continue to still use it?

What email account are you referring too?

If you're talking about your att.net, sbcglobal.net email accounts and then I believe you lose your accounts.

If you're talking about hotmail, gmail, etc.. Then no you will not because they are webmail based and are accessible from any networks ISP.

If you have an email account like hotmail, Yahoo or gmail (anything like that), it won't change. If your email through your provider though?