You say "We installed DBI module of Perl". Please can you give more details.
In particular, did you use the CPAN shell, CPANPLUS, some kind of platform distro (ppm, rpm, apt-get, etc.)
Or did you download DBI from CPAN and follow the README?
The point is that you need to install DBI (which is not included in, but required by DBD::MySQL).
Regarding where you get your Perl from, it is important that you have access to the same C compiler as the one that Perl was built with. Many pre-built perls were compiled with gcc, which is best for most Unix platforms; I don't know about building Perl on AIX because I've never done it. You might need to download and build gcc, see http://directory.fsf.org/devel/compilers/gcc.html
the command perl -V will tell you how perl was built, and with which compiler and linker options. If you can reproduce this on your system, you can use the pre-supplied Perl. Otherwise I would recommend downloading the perl sources off CPAN and building them yourself. This will give you the option of adding XS extensions (external C code) - which is what both DBI and DBD::MySQL require.
Hope this helps
Looks like your Test::Harness is broken. Although this is a core module, it is being actively enhanced and maintained, so I would try getting and installing the latest version off CPAN. But you might be getting more serious problems with other core modules and the 5.6.0 build.
Another possibility is a problem with something in your @INC path - directories, permissions and the like. Can you see a Test/Harness/Straps.pm anywhere there?
perl 5.6.0 is quite old now; it's also quite buggy from what I remember. Release 5.6.1 fixed most of the bugs, and is quite stable. There are further point releases in the 5.6 scheme, but don't contain anything major after 5.6.1.
If you are looking to build a new perl, I recommend going to the latest 5.8.x release, which is 5.8.6 - November 2004.