cannot open output file ut:blib\arch\auto\Cairo\Cairo.dll

This is a bug in ActiveState's mingw-handling capabilities - a bug that has been fixed in more recent builds of ActivePerl.

In C:/Perl/lib/ExtUtils/MM_Win32, try changing:
my $GCC     = 1 if $Config{'cc'} =~ /^gcc/i;
to
my $GCC     = 1;
or, better still (update):
my $GCC     = $Config{'cc'} =~ /\bgcc/i ? 1 : 0;
Apparently $Config{cc} is not matching /^gcc/i. (Is that the case ? What does perl -V:cc produce ?)
Then run dmake realclean and start over again.

UPDATE: Oh ... I see that you're using the latest ActivePerl and the bug is there again. Did you do an upgrade on ExtUtils::MakeMaker ? It's important to use the EU::MM that ships with ActivePerl if you want the MinGW compiler to be handled correctly. The problem is, that with latest builds of ActivePerl, $Config{cc} no longer matches /^gcc/i when MinGW is the compiler. Instead, it matches /\bgcc/i and that's what the MM_Win32.pm that ships with ActivePerl tests for. (The correction hasn't made its way into the EU::MM distributions from CPAN.)

Are things supposed to be this hard?

With older builds of ActivePerl the answer is "yes" unfortunately. Things are much improved with the latest ActivePerl.

Btw, I can currently provide ppm packages (perl-5.12 & perl-5.10) for Glib-1.223, Cairo-1.061, Pango-1.221 and Gtk2-1.222 if that helps.

Cheers,
Rob