So... what class are you using? The standard book class or the srcbook in komascript?
If you're using the standard book class, sectsty has specific commands for the \part command:
\partnumberfont{hcommandsi} Changes the style of part' heading numbers
only; this does not aect the title of the part heading.
\parttitlefont{hcommandsi} Changes the style of
part' heading titles
only; this does not aect the number of the part heading.
\partfont{hcommandsi} Changes the style of `part' headings only by executing
{hcommandsi} before printing each heading; this aects both
the title of the part and the part number.
If you're using the KOMA-script class, the sectsty documentation states:
If you just want to change the fount used for all sectional headings, you
shouldn't use sectsty with any of the KOMA-script classes. Instead, you should redene the \sectfont command provided by the KOMA-script
If you'd like dierent sectional headings to be printed with dierent styles
of type to each other, or if you'd like to underline sectional headings or play
other games that you can't do with the KOMA-script \sectfont command,
then sectsty might be of use with the KOMA-script classes.
You should note that the modications applied by sectsty commands
happen immediately after the \sectfont command is executed.
The documentation for this package is written with the standard LATEX
classes in mind, so might not tie up exactly to the KOMA-script classes.
Despite that, and despite dierences in behaviour when things go wrong,
sectsty should work as expected with the KOMA-script classes.
from: Sectsty Documentation Chapter Four
EDIT: If all you want is a line under your section and chapters, but still want to use the \part command, why not just ditch sectsty, and re-define the sectioning commands in koma-script using \hrule?