If you do end up having to do it the hard way wget has a windows port and will reliably do the URL retrieval for you. It is only 380K when compiled. You could use a short bit of C to exec it, add whatever C you need to check the downloaded file and then use C code like this to display your message box.

#include <windows.h>

int WINAPI WinMain(HINSTANCE hInstance, HINSTANCE hPrevInstance, 
    LPSTR lpCmdLine, int nCmdShow)
{
    MessageBox(NULL, "Goodbye, cruel world!", "Note", MB_OK);
    return 0;
}
[download]

See this if you want to hack on Win32 directly in C. You will find some basic windows URL downloading code in C (only 100 odd lines) here. Essentially the only bit you have to write is the code to do whatever task you want to do with your downloaded data. It should compile into an application under a few hundred K.