usb stick all e mails, as this new computer has only my latest ones, and looking at all mail on it, there are no emails in most of the categories, in most of the saved mails I have on the old laptop.
I hope this makes sense....
Why not just forward/re-send from the old laptop then pick them up on the new one? As you suggest you can transfer them from old to new using the same method on the usb stick, as you did with transferring documents/photo's etc.
Is this webmail or are/were you using an email client?
If you use an email programme that synchronises your desktop with the email server then all your emails received and sent will remain backed up no matter where you are.
It makes things a bit slower but it saves worrying about copying emails back and forth. Which never works all that satisfactorily anyway.
Something to consider for the future.
As you are using GMail they should all be there. I use GMail and it is exactly the same on my 3 pcs, Android phone and iPad.
Have you checked the 'all mail' folder?