Cassa - as mentioned U need to be a bit more specific..
Assume U need to pick up new mail. So U need to be able to open access to the same email as setup on the dead VISTA box (VB).
I would suggest U set up a second email on the laptop in the mail program.
There R 3 elements
1) your = Username/email and password
2) incoming server address : (as per VB)
3) Outgoing server (smpt) address : (as per Laptop)
Server address: i.e. something + domain details - something can be "mail" or "pop" or empty etc. eg. pop.netspace.net.au or mail.domain.com.
You will find the details on your ISP / Mail provider's web site.
Panda is on the money. Most email systems are:
i) A POP type email setup (in most instances) is a "go get msg from the mail box and remove the message" setup. So once you have downloaded it you (& the writer!!) have the only copy.
ii) An IMAP type setup is a "go get copy of msg from the mail box and leave the original" .
So POP relies on your back-up and system, IMAP relies on your mail provider's back-up and system.
I use mail review software on desktop and portable devices - so not limited to one system. I do download to one PC.
(For SOHO setup, I have a number of mail providers and numerous email address's i.e. not restricted to one email address (could not function

). To review and handle these I use MAILWASHER this gives me a heads up on content, sorts & filters, separates out known crap, and allows me to review and handle emails (keep or delete) before I download. There are a number of preview products on the market. I just happened to run into this years ago and like it. )
I would be surprised that current email products are only capable of handling one email address (willing to be surprised

).
If you are not comfortable handling bits from inside a PC & you want to retrieve your existing emails on the VB - follow nebbian's advice.
Otherwise it is fairly straightforward (nerdish comment

) to link to a HDD (Hard Disk Drive) and retrieve the data - but without another similar system to link it to best (timewise at least

) to get help.
Cheers
AP