It depends on how your old machine died. If it is the hard disk that died, then you may (only may) be able to retrieve the pictures, but you will probably need to pay a specialist agency to do it.
However, if the hard disk is fine (and it probably is) then copying the pictures onto the new machine shouldn't be too difficult. The way I would do it, is to remove the hard disk from the old machine (it isn't as hard as it sounds) and then connect it into the new one, boot up and Bob is your mother's brother. This isn't difficult as the insides of computers have dedicated connections and you can't connect things up wrongly (not without a lot of force). However, opening up your new machine will invalidate the warrenty. You might be able to pay someone to do this for you in such a way that the warrenty is preserved. Alternatively, you can get 'USB hard disk connectors'. These allow you to plug the old hard disk into your new machine via a USB port and without taking the back of the new machine.
Failing that, find a mate who is happy enough taking the back off their own computer to copy your pictures onto a CD for you.