Okay, several things here (please forgive me if this sounds patronising, but I don’t know what your level of technical understanding is).
The bad news first: you are highly unlikely to get anywhere with this. Companies like Yahoo! and Hotmail loathe having to spend time surrendering details – remember, they don’t have thousands of staff dealing with the webmail services. They will do so when forced to by legal authorities, and may well take action if the email your friend received was threatening or abusive (most likely simply deleting the account). Since it wasn’t, though, they’re unlikely to give out any details.
Secondly, if the Yahoo! account is anything like my Hotmail account, they have no accurate details on the true user (according to Hotmail, my name is N/A and I live at 1 N/A Street, N/A, N/A). If this is the case, then for Yahoo! to begin tracing the real user, they would have to search through whatever IP logs they keep – a long and arduous task that they won’t start without a good reason.
Okay. So you trace the IP address used to compose the email. The next problem is this: it probably won’t resolve to an actual PC anywhere. The chances are that this person is using a PC at work, through an ISP at home, at school/university or at an internet cafe. In most examples I can think of, the PCs used in these locations usually use DHCP. Since there aren’t enough IP addresses for each PC or network device in the world to have a unique address, companies and organisations buy “blocks” of IP addresses. Assuming that not everyone will be surfing the web at the same time, they then assign these dynamically (DHCP) – so I may have a different IP number every time I connect via my ISP.
If this is the case, then you or Yahoo! would have to go to the ISP or administrator and ask them to go through their logs used to record which IP number was assigned to which hardware ID (the MAC number) at the point when the email was sent. Again, this may be a huge amount of effort for them.
And, lastly, even if you know which physical PC the email was sent from…well, you still don’t know who the user was. If it was at an internet cafe or a university PC lab, you’re out of luck.
Sorry to be a downer, but I really doubt that Yahoo! will play ball.
I’m sure it’ll be on the market soon, though, at which point, you can use it to trace your friend’s admirer back to his/her home computer. It may even tell you what he/she looks like!