Transferring data (& iTunes, iPhoto etc.) from old spoilt mac to new?

Hi, I got a new MacBook recently but all my data and my iTunes & iPhoto library are in my old one, which I can't even start up - it's completely unresponsive when I try to turn it on. And unfortunately I didn't back it up while was still working, even though it was clearly steadily deteriorating even after I got it repaired once… Do I have to get it repaired again in order to retrieve all my data? Apart from the data, is there a way to start up my iTunes library exactly the way it was before (I had 600 songs but the files are all in my old computer…) so I can regularly sync it with my iPhone again? If I'm not wrong, iTunes only syncs in one direction, so do I have to wait until I can use my old computer (and how do I do so then?) Any related tips are greatly appreciated!

Are you handy with a screwdriver?

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