The problem is probably that the operating system on your new computer is incompatible with your old CS4 software. CS4 is old and end-of-life, is receiving no new updates and no support.
What operating system on your new computer?
CS4 is not supported under El Capitan.
In fact, no version earlier than CC2015 is supported. I’m afraid your own.
That said, if you used migration to get these apps installed, you should uninstall them, use the CC Cleaner tool and then reinstall them properly. No assurance but it might get you running at least.
OS10.11.4 It worked on my last computer which had the same operating system.