Many people have discovered what you've just found: The current Mac OS X operating system is NOT guaranteed to support an older application like InDesign CS4, which was created long before. You'll either have to find another old computer with an older version of OS X, or upgrade to InDesign CS6 or CC.
No, InDesign CS4 runs on 10.9. I run it on my MacBook Air, on 10.9, as CS5.5
@alc321, did you reinstall InDesign from original DVD (or downloaded installer), or did you migrate your files from your old computer to your new one? This does not work with Adobe applications, use your original installer.
I did migrate files so i will try a disk install before i give up. I did find however that Pages has enhanced their graphic arts abilities that i can get some things done. Thanks for your suggestion!
Sometimes migrating an InDesign installation to OSX 10.9 will work. I have a customer who lately did that with InDesign CS5 and astonishingly it worked for him (OSX 10.6.8 => OSX 10.9.?). I would have never adviced him to do so. Also all other apps in his CS5 Design Suite did work. Was it by chance? Fingers crossed, that he could work on flawlessly…