The question was answered by Daniela Osterhagen in a Google+ post that is no longer available:
It's probably the indycore.dcp file that the compiler cannot find. Is that file in the library path?
No, it's not! Look at the command line you posted! It doesn't contain c:\delphi\delphi2010\lib\indy10 !
I just temporarily removed that directory from the library path in my Delphi 2010 installation and got the same error.
As it turned out, that was exactly the problem. $(BDS)\libs\Indy10 was missing from the library path. I have no idea how that came to happen, because as said above, this was a fresh install.
(links removed, Google+ is no longer available and the Internet Archive hasn't got them either)