You never said whether your hard drive is dead. If it's not, pull it out and use it as an external drive (with the help of a SATA-Firewire adapter). Use Migration Assistant.app to copy over your music, or just copy your iTunes folder (e.g., "~/Music/iTunes Media/").
Then, the next time open up iTunes, hold down alt as you tell it to open. In the following dialog box, select the new location of your iTunes Media folder.
My apologies if your hard drive is legitimately dead. I don't yet have privileges to comment on a question, which would have been a more appropriate vector for asking you to clarify the state of your hard drive.
In iTunes, on your first machine, you will have to go to File|Library|Export Library.
This will generate your Library.xml file.
If you take a look in it, you will see for each file all the fields you will find in iTunes (location on HDD, play count, rating, etc...).
Now, on your new machine, after having installed iTunes, you have to go to File|Library|Import Playlists (not obvious at first as I was looking at an Import Library menu but it doesn't exist) and select the xml file you exported on your first machine.
If you try, as I did first, to edit the xml file and overwrite the newly created one, when launching iTunes, it will delete it and create again an empty new one. You have to go through this Export/Import process (which is quite quick).
PS: you may have to edit the xml file anyway before importing, if the paths to the music files changed from your initial machine. For example, I upgraded from WinXP to Win7. As the user folder path changed, I then had to edit the paths c:\users and documents\myuser\My Documents\My music to c:\users\myuser\Music, or something like that, I don't remember exactly.
PPS: Always keep your exported xml file untouched somewhere until you have everything OK on your new machine...
Best Answer
You have two options:
If you have enabled iTunes Match, you will also be safe from most data loss since all playlists are stored in the cloud unless it contains exclusively tracks that were not matched to the cloud like podcasts and other oddities like voice memos and low bit-rate recordings.