You really need to find a way to get your old files and account copied from the old Mac to the new one. If you can't do that alone, try the Apple store.
"Died" doesn't usually mean all your data is gone...it's just a little harder to get at. Probably someone else can do it for you.
(And yes, buy an external drive and use Time Machine from now on. That'll save you this trouble next time.)
You can save everything except music (which isn't a big deal unless you didn't back it up)
You can get contacts back by merging, transfer purchases (apps and videos, songs etc)
I re-installed OS X this weekend and forgot about my iPhone..I was worried about contacts, but I plugged into iTunes and merged data with address book and it's all good :> I then transfered purchases (file, transfer purchases) and besides music, my phone was like it had been 🙂
If at all possible, I would pull the drive and copy the files off onto your new machine.
I would want at least my:
Music Folder
Pictures Folder
E-Mail
Address Book
Documents
There are other valuable files in your user folder, but those would be the minimum I would want. You can pull the music off your iPhone with some of the third party applications, but it will be much more complete if you can get to the hard drive in your "dead" computer...
Once you have everything, you can even use your old drive in the new external enclosure for Time Machine, and make sure you have a backup from now on...
Unless I missed something or a post, IDKY no one suggested using sharepod, which is free, or a similar program to get the music, movies, and pictures off the iPhone. You can use Funambol, also free, to upload the contacts online.