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Hello Carolyn how are you today? I can try to assist you with this.
As far as the emails, are you storing them on your machine, or do you go to a website to view them? He could try exporting the emails from your older machine, and ensure it does not include the "Trashed" emails. What email client are you using?
As far as files, most files are kept on the desktop, or in My Documents. Usually just copying these over may be the easiest way (with a USB) but it seems your bigger concern is the emails so we can focus on that for now.
Let me know if you are having trouble with any of this and I will assist.
For your email depending who the service provider is, for example -- ***@******.***
It would be easier (if the emails are not deleted) to set up your new email client to re-download the emails instead of exporting and importing them from one machine to another.
I am here to assist you if you would like further help, please let me know!