Take this with a grain of salt. I think it's correct, but I haven't done this. It's quite untested. Use at your own risk. Backup everything first. You've been warned.

Both hardburn and PodMaster are correct - you've got to have parts of the MySQL server installed before you can install DBD::Mysql. (hardburn called them "MySQL development headers" and PodMaster called them "mysql client libraries.")

To do this, download the source tarball for MySQL from here.
(Since you're using Cygwin, I'm not sure if you should get the "Tarball" or the "Windows Source")
Untar/unzip it somewhere in your Cygwin tree.
CD to the directory you just created.
Now try:

./configure --without-server
make
make install
[download]

That should install enough of the MySQL client to allow you to install DBD::Mysql (I think ...).

I hope that helps, at least a little.

Cheers,

Brent

-- Yeah, I'm a Delt.