You seem to have two options: fix ppm or use cpan.

The fact that you can access cpan to find the modules implies that you have internet access so, unless a firewall is blocking it, ppm ought to work. As a sanity check you could ensure that the ActiveState package repository is set to http://ppm4.activestate.com/MSWin32-x86/5.10/1006/package.xml in the PPM Preferences.

If ppm isn't fixable you can use cpan from the command line to install the modules you need. Just:

cpan DBD::mysql
[download]

although that will probably require you to install mysql first so that the headers and library files are around that are required to build the module. The first time you use cpan it will most likely download and install the mingw compiler too, but at least it just does the right thing - that much is pretty smooth.

However, I strongly recommend that you try to get ppm going first. If you are unsure about how everything works you will find using cpan to install modules much more intimidating (initially at least) than using ppm. Oh, and I can pretty much guarantee that the cpan install of DBD::mysql will not go smoothly!