I recently added a page on Lua WIKI (great source of info) that may help you. It is a tutorial for complete newbies on how to build Lua from the sources using only free and "portable" (in the sense of "can be put on usb drives") tools. It is meant for Windows OS users. Do not forget to check the official getting started page and the main Lua site as well!
The fact that you cannot download anything is quite restrictive (how could you get a free compiler then?). Anyway as greatwolf mentioned TDM-GCC is a great C/C++ compiler for 32 bit x86 PCs. It is also patched to be perfectly "portable": I usually use it from a portable USB HD. The tutorial I mentioned shows you how to download it and "install it".
Note that although your sysadmin at school may have blocked your ability to change the path variable globally, you can set it for individual processes ("launched programs") using simple batch files (aka Windows command shell scripts).
Create a file named "myshell.cmd" with this content:
@set path=%path%;c:\the\path\to\my\app&cmd /K
the part c:\the\path\to\my\app
must be the actual path of the directory (folder) where the application executable is placed. When you double-click on myshell.cmd
a black box will open (assuming your sysadmin hasn't blocked this feature) where you can invoke the app executables.
For example, if you "installed" the TDM_GCC compiler in c:\myprogs\GCC
inside that dir you will find a subdir named bin
. That subdir must be put in the path, so your myshell.cmd
file will be like this:
@set path=%path%;c:\myprogs\GCC\bin&cmd /K
Then in the "black box" I mentioned you can invoke the compiler typing:
gcc --help
As for your learning path, if you intend to learn both Lua and C or C++, I will advice you to try C instead of C++. C++ has more "high-level" features, but it is huge and although Lua can be used embedded in C++ code (of course this is an advanced topic anyway), it is designed to be directly embedded in a C application (it has an API which conforms to C conventions), so for a beginner probably the path Lua --> C --> C+Lua would be a bit easier. C in itself, although difficult to master, is a rather minimalistic language, so the information to digest about it is not that big.
Not to discourage you, but IMO both C and C++ are not the most suitable languages for absolute beginners (they are plenty of pitfalls and have almost no "safety nets" for beginners). But that's up to you, it heavily depends on your skills, dedication and motivation ;-)
Hope all this helps.