retrieve emails from a dead Outlook 2010 account....please

I could really use some help please. I had an Outlook 2010 account as a contracted person with the UN and they killed the account and decided to use a gmail account (I have no idea why!). I would like to get all my emails (folders too if possible) on, say, a USB stick and then put it on my new work computer.

I tried the Export function but you need to sign in and the account doesn't work. So, can I copy the outlook.pst file or even all of the .pst files and then open them somehow in another computer with Outlook?

I don't want to use these anymore to contact or respond, I just want to have the messages and the addresses of the people who sent them to me and my outgoing messages and conversations too.

So what can I do here?

Thanks a lot!

Yes you can point your Outlook data file to the pst you have. As long as your Outlook version is the same or higher.