You did not mention which program version you are using and which Computer with which OS version is used. This information would be important to know if both are compatible or if you have to buy or upgrade InDesign.
That is true, but the activation server is also forgetting after several Years, and CS2 is not supported by the server anyway.
2004 could be CS or CS2 way to old for activation.
If it was 2004, then you probably bought CS2, no? LIke WIlli says, that's half of the information we'd need to answer your question. The other half would be the version of Mac OS you're using.
Both your MacBook Air and your new iMac have Intel processors. Your new iMac (assuming that it's new new, and not just new-to-you) is running a version of OS X that is too new to have Rosetta support for CS2, which was a PPC-only application. So, it really boils down to this: Is your MBA running Snow Leopard? If you don't have Snow-Leopard-or-older installed on one of your Macs, there are technical problems that will keep you from being able to install CS2.
You should tell us what error messages you get when you try to install; that will help us figure out which of the above is the problem.
Lastly: I run lots of old software on brand-new Macs, by virtualizing an old install of OS X, e.g. running OS X 10.5 inside of OS X 10.8. It's not trivial to get it running, but it's totally doable. There are many cheap and/or free solutions, here. It'd be easiest if, when you found your old CS2 disk, you found an old Leopard or Snow Leopard disk at the same time.
Edited: to remove commentary about activation, because oh yeah they shut down the CS2 activation servers.
If you bought InDesign in 2004, it was obviously the first version of Creative Suite,
InDesign CS only ran on Power PC Macs
SInce 2006 all Macs have run on Intel chips.
Apple had an emulation module called Rosetta to allow the newer Intel chips to run older Power PC only software.
All major applications have been rewritten to run on Intel chips and the last version of Mac OSX to have Rosetta was Snow Leopard 10.6.8
Your newer Macs cannot run old applications like InDesign CS.
You only current choices are to buy InDesign CS6 at full price - this is the last version that you can use as long as you hardware/OS supports it, or buy a subscription to Adobe Creative Suite which is a monthly subscription. You can buy just a single application but it is still a subscription,
So if you stop paying the software stops working.