I have done a whole lot of testing now with a blizzard of HQ versions, JRE versions, etc.
It appears that on this system SIGAR is not picking up the fact that pdh.dll is present in the %HQ_HOME%\pdk\lib directory, even though it's sitting right there. This is true for any JRE (original, as-shipped, v1.5.0_07 and v1.6.0_05), with any version of HQ 3.1.4 and above.
Placing this pdh.dll file into the %SystemRoot%\system32 (the default dll path for the whole environment) resulted in HQ v3.2.3 happily humming away.
Checking other Windows 2003 Servers with functioning HQ shows that a current version of pdh.dll is present in the %SystemRoot%\system32 directory on all of them. Only this one box was missing the file.
With that said, I took a look at the pdh.dll that's being shipped with the HQ agent, and it's an old one from Windows 2000. Removing it entirely from %HQ_HOME%\pdk\lib doesn't seem to affect the operation of HQ, so perhaps it's no longer necessary to ship it?