I've always thought Half-Life was in C, not C++. Quake II was in C, that I know, and so was Quake. And since Half-Life uses either the Quake or Quake II engine (Can't remember which), it's coded in C if I'm not mistaken.
But yah the other part what Majin_You said is correct. Newer games are coded in C++.
I believe Valve used Microsoft Visual C++ 5 to create and compile Half-Life.
From what I've read Half-Life is based on Quake 1, with a small amount of Quake 2 code.
The map compilation tools that ship with Half-Life are called the "q-tools." One guess what the 'q' stands for.
The Half-Life SDK is written in C++, though some of the primitive engine and movement functions were written in C. I'm assuming that's because they were taken from Quake, but I've never worked with the Quake source, so I wouldn't be able to identify what was used and what wasn't. I've seen a few particle effects taken directly from Quake, that's about all I've recognized.