Hi Geertjan,
Please compare the folders, on the previous and the new Mac. There is a Folder “resource”, inside of it you might have one or more ‘string_…” folders. The “...” stand for the language: two letters.
Normally it should work when you move just the whole folder to the new harddrive. The simplest way would be via USB-stick, or while you are on Mac, use a firewire cable, restart the previous computer while holding down the T key, which puts this computer in disk mode and it shows up on the new one as disk. You might even try to start from that disk C4D to see if it works.
Anything else should be discussed with the support. http://www.maxon.net/support/support-questions.html
To install newly is certainly never a bad idea, except for the time you have to invest.
My best wishes and congratulations for the new Mac.
Sassi