When your old computer has crashed, you can retrieve your Outlook pst files (and other files and documents) as long as you can connect the old hard drive to the new computer. The easiest way to do this is with a USB enclosure for the old hard drive. You can find these at many electronics stores or online. They come in two formats: a case the drive slides into, so you can easily carry it around or just the connectors (and a power supply) you need to connect the drive to another computer.
Once the old drive is connected to the new computer, open Windows Explorer (aka File Explorer) and browse the old drive.
If using Outlook 2010 or newer, the pst files are stored in a folder named Outlook Files in your Documents (or My Documents) folder.
If the old computer used Windows XP and an older version of Outlook, the default location of the old pst files will be
[new_drive_letter]:\Documents and Settings\username\Local Settings\Application Data\Microsoft\Outlook
If the old computer had Windows 7 or Vista or newer with an older version of Outlook, the default location is
These are hidden files and folders and are most likely protected by permission settings. To change the permissions, right-click on your old username folder and choose Properties.
On the General tab, if "Hidden" is checked, deselect it and click Apply.
On the Security tab, click Edit, then Add and give either your new user account or Everyone "Full Control" and click Apply. (The old computer account displays as Account Unknown.)
If "Hidden" was not checked, you can either change the Hidden Files and Folders setting in Windows Explorer (at Organize, Folder and Search Options, View) or select the next folder(s) in the path and right-click, choose Properties and deselect Hidden.
Now you can browse down the folders to locate your Outlook pst files and copy them to the new computer. If the pst files use the new Unicode format (introduced in Outlook 2003), you can use this pst in your new profile.
If it's the older ANSI format pst file, you can use File, Open, Import to import it into Outlook 2010.
Don't bother moving .*ost files, which are used by Hotmail Connector and Exchange server mailboxes. You won't be able to open these files on the new computer. If, for some reason, you need to recover data in .ost files you'll need to purchase recovery software.
While the old drive is connected, browse the user folders for files you may want to move, including your custom dictionary and support files Outlook uses. See Moving Outlook to a New Computer for the Outlook files you might want to move and where to find them, along with instructions to configure Outlook with the old data files.