I want the \parttitle displays in the header, however, as you see on the picture below, this command has been ignored:

I tried solutions from there questions:
The MWE is...
\documentclass[a4paper,twoside]{article}
\usepackage{titletoc}
\usepackage[pagestyles]{titlesec}
\newpagestyle{myfancy}[]{\headrule\setheadrule{0.5mm}\footrule\setfootrule{0.5mm}}
\begin{document}
\pagestyle{myfancy}
%\sethead[\thepart\:\parttitle][][\thesection\:\sectiontitle]{\thesection\:\sectiontitle}{}{\thepart\:\parttitle}
\sethead[\thepart\quad\parttitle][][\thesection\quad\sectiontitle]{\thesection\quad\sectiontitle}{}{\thepart\quad\parttitle}
\setfoot[\thepage][][]{}{}{\thepage}
\part{Part A}
\section{Section AA}
\subsection{Section AA}
\subsubsection{Section AAA}
\subsubsection{Section AAB}
\subsection{Section AB}
\subsubsection{Section ABA}
\subsubsection{Section ABB}
\section{Section AB}
\end{document}
Please, keep the titlesec package usage in your solution.
After I corrected according Mr. Werner answer and returned to my source file
I discovered that hyperref package and redefining part with titlesec commands has influence, too. Look the MWE below: the part will not display if you place \usepackage{hyperref} before \usepackage{etoolbox}. It's simple to correct, however if you need to redefine the part with titlesec commands, \parttitle will dissapers again. Is anything possible to do with it? (Please don't forget to remove \iffalse from row 28 to make \parttitle disappear again)
\documentclass[twoside]{article}
\usepackage{titletoc,etoolbox}
\usepackage[pagestyles]{titlesec}
\newpagestyle{myfancy}[]{\headrule\setheadrule{0.5mm}\footrule\setfootrule{0.5mm}}
\usepackage{etoolbox}
\makeatletter
\patchcmd{\@part}% <cmd>
{\markboth{}{}}% <search>
{\gdef\parttitle{#1}}% <replace>
{}{}% <success><failure>
\makeatother
\usepackage{hyperref}
\pagestyle{myfancy}
%\sethead[\thepart\:\parttitle][][\thesection\:\sectiontitle]{\thesection\:\sectiontitle}{}{\thepart\:\parttitle}
\sethead[\thepart\quad\parttitle][][\thesection\quad\sectiontitle]{\thesection\quad\sectiontitle}{}{\thepart\quad\parttitle}
\setfoot[\thepage][][]{}{}{\thepage}
% ---------------------
\usepackage{color,tikz}
\usetikzlibrary{arrows}
\usetikzlibrary{shadings}
\usetikzlibrary{fadings}
\iffalse
% -- Part format
\definecolor{ChapterColor}{rgb}{1.00,0.80,0.61}
\definecolor{ChapterColor2}{rgb}{0.5,0.10,0.23}
\tikzfading[name=fade up, top color=transparent!0,top color=transparent!100]
\titleformat{\part}[display]{\Large\sffamily\color{ChapterColor}}
{\filright\Huge\sffamily\bfseries \hspace*{2mm}%
\begin{tikzpicture}[baseline={([yshift=-.6ex]current bounding box.center)}]
\node[fill=ChapterColor2,rectangle,rounded corners,text=white] {第\thepart 部};
\fill [yellow,path fading=fade up] (-2,-1) rectangle (\columnwidth-22mm,1);
\end{tikzpicture}}
{1ex}
{\titlerule[1.5pt]\huge\sffamily}
[]
\titlespacing{\part}{0pt}{0pt}{2mm}
\titleformat{name=\part,numberless}[display]
{\normalfont\color{ChapterColor}}
{}
{1ex}
{\vspace*{5ex}\huge\sffamily}
[]
\fi
\begin{document}
\part{Part A}
\section{Section AA}
\subsection{Section AA}
\subsubsection{Section AAA}
\subsubsection{Section AAB}
\subsection{Section AB}
\subsubsection{Section ABA}
\subsubsection{Section ABB}
\section{Section AB}
\newpage
\part{Part B}
\section{Section AA}
\end{document}

\markboth{}{}? If you add a part B followed by a few pages of lipsum before the next section, you'll still get section references from part A. At least, that is what seems to happen. – cfr Oct 14 '14 at 01:24