A workaround that seems to have worked for a few others is to install the Outlook Hotmail Connector on the system with Outlook and through the connector add the Outlook.com account to Outlook. Email can then be copied over or imported from PST within Outlook and synchronized with Outlook.com. Once it is in the cloud at Outlook.com it will be accessible anywhere, including the Windows 8 Mail App. There are a few issues noted in the thread, such as issues with folders of emails resulting in errors when syncing, but if the PST file is already backed up, there is no harm in trying.
Suspect you'll need to install Outlook on your new machine and use the Import/Export in the File Menu. Outlook exports files as *.pst and these are not recognised by Live Mail. (I just tried!)
A workaround that seems to have worked for a few others is to install the Outlook Hotmail Connector on the system with Outlook and through the connector add the Outlook.com account to Outlook. Email can then be copied over or imported from PST within Outlook and synchronized with Outlook.com. Once it is in the cloud at Outlook.com it will be accessible anywhere, including the Windows 8 Mail App. There are a few issues noted in the thread, such as issues with folders of emails resulting in errors when syncing, but if the PST file is already backed up, there is no harm in trying.