Here's a way to indent the final block by limiting the scope of the \setlength{\parindent}{0pt}
and adding an explicit skip at the start.
\documentclass{book}
\usepackage[turkish]{babel}%türkçe karakter
\usepackage[utf8]{inputenc}
\usepackage{textpos}
\newcommand{\fromtop}[1]{\dimexpr-1in-\topskip-\topmargin-\headheight-\headsep+#1\relax}
\newcommand{\fromleft}[1]{\dimexpr-1in-\oddsidemargin+#1\relax}
\begin{document}
\begin{titlepage}
\begin{textblock*}{\paperwidth}(\fromleft{0cm},\fromtop{3cm})
\centering
\textbf{ASDGGSDFG ÜNİVERSİTESİ\\
DASDGG ENSTİTÜSÜ}
\end{textblock*}
\begin{textblock*}{\paperwidth}(\fromleft{0cm},\fromtop{6.5cm})
\centering
\textbf{DHFGHDH ANABİLİM DALI}
\end{textblock*}
\begin{textblock*}{\paperwidth}(\fromleft{0cm},\fromtop{9.5cm})
\centering
\textbf{ASGFHFDHDGH\\
DFHSGFHDFHG}
\end{textblock*}
\begin{textblock*}{\paperwidth}(\fromleft{0cm},\fromtop{15cm})
\centering
\textbf{DOKTORA TEZİ}
\end{textblock*}
\begin{textblock*}{\paperwidth}(\fromleft{0cm},\fromtop{16cm})
\centering
\textbf{adgdfhf}\\
\textbf{124356}
\end{textblock*}
\begin{textblock*}{\paperwidth}(\fromleft{0cm},\fromtop{19.5cm})
\centering
\textbf{Tezin Savunma Tarihi : 00.00.0000}
\end{textblock*}
\begin{textblock*}{\paperwidth}(\fromleft{0cm},\fromtop{23cm})
\centering
\textbf{Tez Danışmanı : asdf}
\end{textblock*}%
\begin{textblock*}{\paperwidth}(\fromleft{4cm},\fromtop{26.5cm})
\hskip \parindent Bu Yüksek Lisans/Doktora Tez Çalışması FDGSDFGHH Üniversitesi\\………………’nolu Proje ile desteklenmiştir.
\end{textblock*}
\end{titlepage}
\end{document}
If you need to alter the spacing of the text within this block, you could load the setspace package. You can then use
\begin{singlespace}
<content>
\end{singlespace}
\begin{onehalfspace}
<content>
\end{onehalfspace}
\begin{doublespace}
<content>
\end{doublespace}
for single, 1.5 and double spacing or
\begin{spacing}{<whatever>}
<content>
\end{spacing}
if you need a different value.
It is not clear what you mean by changing the text height. The \textheight
is the height of the entire text block i.e. everything except the margins, so obviously cannot be changed for only part of a page.
EDIT
I'm still not entirely clear how the last block should be formatted. Do you want something like the following?

The final block here is formatted like this:
\begin{textblock*}{\paperwidth-80mm}(\fromleft{4cm},\fromtop{26.5cm})
\begin{doublespace}
\large Bu Yüksek Lisans/Doktora Tez Çalışması FDGSDFGHH Üniversitesi\\………………’nolu Proje ile desteklenmiştir.
\end{doublespace}
\end{textblock*}
As mentioned by egreg, we can actually drop the zeroing of the \parindent
as all blocks except the last are centred anyway. So we can just let the natural paragraph indentation indent the first line.
\large
increases the font size, relative to the document default.
Changing the width of the text block ensures that it has 4cm indentation on both the left and right sides of the page.
Complete code:
\documentclass{book}
\usepackage[turkish]{babel}%türkçe karakter
\usepackage[utf8]{inputenc}
\usepackage{textpos,calc,setspace}
\newcommand{\fromtop}[1]{\dimexpr-1in-\topskip-\topmargin-\headheight-\headsep+#1\relax}
\newcommand{\fromleft}[1]{\dimexpr-1in-\oddsidemargin+#1\relax}
\begin{document}
\begin{titlepage}
\begin{textblock*}{\paperwidth}(\fromleft{0cm},\fromtop{3cm})
\centering
\textbf{ASDGGSDFG ÜNİVERSİTESİ\\
DASDGG ENSTİTÜSÜ}
\end{textblock*}
\begin{textblock*}{\paperwidth}(\fromleft{0cm},\fromtop{6.5cm})
\centering
\textbf{DHFGHDH ANABİLİM DALI}
\end{textblock*}
\begin{textblock*}{\paperwidth}(\fromleft{0cm},\fromtop{9.5cm})
\centering
\textbf{ASGFHFDHDGH\\
DFHSGFHDFHG}
\end{textblock*}
\begin{textblock*}{\paperwidth}(\fromleft{0cm},\fromtop{15cm})
\centering
\textbf{DOKTORA TEZİ}
\end{textblock*}
\begin{textblock*}{\paperwidth}(\fromleft{0cm},\fromtop{16cm})
\centering
\textbf{adgdfhf}\\
\textbf{124356}
\end{textblock*}
\begin{textblock*}{\paperwidth}(\fromleft{0cm},\fromtop{19.5cm})
\centering
\textbf{Tezin Savunma Tarihi : 00.00.0000}
\end{textblock*}
\begin{textblock*}{\paperwidth}(\fromleft{0cm},\fromtop{23cm})
\centering
\textbf{Tez Danışmanı : asdf}
\end{textblock*}%
\begin{textblock*}{\paperwidth-80mm}(\fromleft{4cm},\fromtop{26.5cm})
\begin{doublespace}
\large Bu Yüksek Lisans/Doktora Tez Çalışması FDGSDFGHH Üniversitesi\\………………’nolu Proje ile desteklenmiştir.
\end{doublespace}
\end{textblock*}
\end{titlepage}
\end{document}
\textheight
for just one block of text on the page because this dimension is the height of the entire text block for the page i.e. everything except the page margins, header, footer and so on. – cfr Jan 10 '16 at 0:28