I'm new to TR-Anniversary - just beginning.  I can't seem to even connect with the 2nd grapple in the game after spending almost an hour trying.  Is there something I can do to get moving and on to actually opening the doors?

You don't mention what platform you are playing on, but I can tell you, it's best to master the grapple now than to wait for later in the game.

As with all TR "stunts" and timed runs, practice, practice, practice.

Good luck!

If I remember right, you need to hold the key so that the grapple locks and then you can pull.... should play the game again... lol