In sounds to me like you may want to have the contents of your old .pst file.
You can perform a search on your old computer for *.pst
That should come up with at least one if not more.
You can transfer it or them off onto external media and then use Outlook on your new computer to open them and examine their contents to see if they contain what you are looking for.
Use the "export" feature under the "File" tab to export your .pst files to another removable drive and then import them into your new Office program the same way.
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