No, I am linking with the static version.  The problem was curl 7.37.0 didn't include a project file I could tweak and so had to use the makefile to buld the static lib with nmake.  And that makefile apparently has some stuff wrong.
Anyway, your curl_static.lib links perfectly.
Edit: I found the latest version's VS2008 project files, they were under projects/Windows instead of under lib/.  I found that the projects were set compile as C++ code using the DLL runtime libraries- obviously I changed that to C and non-DLL runtime libraries.  I also added those libs you listed to the Additional Dependencies under the Librarian/General section of the project's Configuration Properties.  And now the library I compiled links perfectly, too.