The app I'm trying to build is my app, and I've built it before, but it's been three years, so I'm sure I've forgotten a lot. My old laptop's hard drive died, so I'm trying to set up a new Windows BOINC build environment, with either VS 2008 express or 2012 express. I built the API without problems (three things I think, including _staticcrt in some cases.) But when I try to link in BOINC 6.10.17, I get:

m:\boinc\api\boinc_api.h(136) : error C2146: syntax error : missing ';' before identifier 'worker_thread_handle'
m:\boinc\api\boinc_api.h(136) : error C4430: missing type specifier - int assumed. Note: C++ does not support default-int
m:\boinc\api\boinc_api.h(136) : error C4430: missing type specifier - int assumed. Note: C++ does not support default-int
C:\Program Files\Microsoft SDKs\Windows\v6.0A\include\winnt.h(334) : error C2378: 'HANDLE' : redefinition; symbol cannot be overloaded with a typedef
        m:\boinc\api\boinc_api.h(136) : see declaration of 'HANDLE'
C:\Program Files\Microsoft SDKs\Windows\v6.0A\include\winnt.h(340) : error C2143: syntax error : missing ';' before '*'

And many similar errors for HANDLE, GLOBALHANDLE, LOCALHANDLE, etc. I think it's all related to those terms being redefined in BOINC's header files. I tried substituting in the .NET Framework 3.5 SP1 SDK files, and it had no effect - though I didn't try rebuilding the BOINC libraries that way.

What am I doing wrong?

You should always link against the latest BOINC libraries. There are some bugs and enhancements within the last 3 years. The windows boinc_depends are also in another repository: http://boinc.berkeley.edu/trac/browser

I don't have a Windows build env so I can't help more. Better help could be found in the boinc_dev mailinglist.