Sync Outlook with Webmail?

[RJrules64]

Hi, I recently upgraded my Windows XP computer to a Windows 8 computer.

I had Outlook 2003 on my old computer, which isn't compatible with windows 8.

I don't have the money to purchase a newer version of outlook, So I signed in to my optus webmail.

I can receive new emails, but cannot see any of the old emails I looked at in Outlook.

I still have my old computer with Outlook, So if need be, I can transfer all my old emails onto my new computer. What is the process for this?

I also tried to log in to the mail app in windows 8 but that didn't seem to work either.

Please help! Thanks