I suspect you will be as thwarted trying to install CS4 as you were with your CS6 key. CS4 reached its end of life a long, long time ago, and any servers needed to finalize the installation that would have been active when CS4 was have long been turned off, for one, and for two, your current computer operating system will most likely not be compatible with the software and disallow the installation. For three, your CS6 key is unique to your copy of CS6--which also has basically passed end of life. Most likely, your only real option is a Creative Cloud subscription or switching to the free but bloated Brackets or maybe Wappler.
Nothing you can do. Your CS6 serial number is not compatible with CS4 and vice versa.
Chris is partly right. CS1, CS2 and CS3 activation servers are officially dead and gone. However, CS4, CS5 and CS6 activation servers are still online but the products themselves are on life support. To use outdated software, you need the following:
1. the original installation disks,
2. a legitimate serial number for that particular product, version and platform (Win or Mac),
3. a supporting operating system that can run legacy Creative Suite software.