if you want to recover anything from that computer, it must have been stored on the hard drive at some point in time...
hotmail/yahoo: you might find something in temporary internet files, but that's a longshot.
outlook express: it keeps emails in files with the DBX extension. i believe they are in Application Data in a user's home directory.
chat conversations: unless they were logged to a file, you're out of luck.
if you work in law enforcment, then it's no problem to contact the ISP and ask for the addy in questions email log, they have to backup everything by law, as you already know.
as for the chat log, if it's been deleted, then your high tech crime unit will be able to recover deleted data.
kinda makes me wonder why you would be asking on a internet tech site when you have so many resources in the police department at your disposal.