Non-Root Package Managers
I'm stuck with a pretty old Linux distribution at work (Centos 5.4 from the end of 2009), and also don't have root access. If I want to use more recent software, I can compile it myself and install it my home directory (or somewhere where I have write access). That works fine with many programs, but it gets complicated with bigger ones (such as LibreOffice or Chromium). It is pretty complicated to track all the dependencies.
I'm wondering if someone did this before, and maybe built a sort of Linux* distribution that I can install in my home directory (without root), and that brings all the needed dependencies with it. Preferably as binaries, as that would make it a lot faster and easier to install on an old machine. But I'd also take a 'ports' like system, or even just tips how to organize stuff if I have to compile it all manually.
*) Note to nitpickers: of course this wouldn't be a Linux distribution technically, since the one thing missing will be the actual Linux kernel.
Before someone says this is not possible, I know it is possible, at least in most cases. For one, a lot of Linux libraries are backwards compatible, although this is not used nearly as much as in Windows (where there is no package manager). Second, you can compile most libraries needed yourself, the only thing you can't replace is the kernel. You can force the new libraries via LD_LIBRARY_PATH, or when compiling the programs that shall use them. I've managed to install a recent Skype some time ago, which needed a newer version of glibc. There even used to be someone who maintained Chromium with all its ridiculous dependencies for this version of CentOS. It's certainly possible, but its unwieldly, and seems like an ideal task for a computer program / distribution / package manager.