Two questions:

I'm trying to launch AoW2, and the game is demanding a password. Guessing and hoping that this was not a registration number that was supposed to be supplied, I tried just entering in my own password, and that failed to launch the game.

1. Were passwords supplied by Gog, and if so, how are they accessed?

2. How can I set a download to a different drive? The C drive is getting full, but there does not appear to be any way to alter the default.

The GOG installer has a neat little button named "Options", there you can change the install path.
And you can download to whichever folder or drive you want, it depends on your browser settings.

Looking at the text file on the left maybe better not ;-)

@bearcat: You should better crop your image that only the message-box is visible. I can't really help you, but I don't believe the problem belongs to the path (it seems you're running WinXP, so no problems with right-management). Do you have installed another version of AOW before? Than maybe an old registry-key is the reason for the serial-number request (just my guess).

The reward outweighs the risk. :P

Regarding the OP's problem I don't know. What I would have done in his place is to check if any image program like powerISO or something similar is messing with a old copy protection in AOW and check my registry. You could use a registry cleaner program but I'm loathe to advice that because they can seriously mess up your system.