Chillblast computers are supplied with very little software indeed as I recently found out. You will need an e-mail client to replace Outlook Express. The Microsoft equivalent is Windows Live Mail Live Essentials which is part of Windows Live Essentials. You do not have to download all of Live Essentials just choose (tick/untick) the parts you want. Be careful about Bing with it. Then you set it up for the e-mail accounts. It would be useful to make a note of the password and settings from the old computer.
If you want to transfer the old e-mails over that can be done too.