BELOW_NORMAL_PRIORITY_CLASS and its sister ABOVE_NORMAL_PRIORITY_CLASS were introduced at Windows NT 5.0, sorry, Windows 2000. A lot of Win32 code is built for the more generice NT 3.5.

From the Win32::Process Changes file (on CPAN):

0.13  Fri Jun 13 2008

    ...
    - Add ABOVE_NORMAL_PRIORITY_CLASS and BELOW_NORMAL_PRIORITY_CLASS
      constants (not exported by default).

    ...
[download]

So it looks like you need a later version for these constants. I have not tried this, but it is possible you could declare your own:

BELOW_NORMAL_PRIORITY_CLASS       0x00004000
ABOVE_NORMAL_PRIORITY_CLASS       0x00008000
[download]