At the begining of a new chapter the plain page style is used by default. If you want headers on chapter pages also, you may have to redefine the pagestyle plain.
\documentclass[12pt, bibliography=totoc]{scrreprt}
\usepackage{ngerman}
\usepackage[T1]{fontenc}
\usepackage[isolatin]{inputenc}
\usepackage{graphicx}
\usepackage[german]{varioref}
\usepackage{moreverb}
\usepackage{lastpage,lipsum}
\usepackage{fancyhdr}
%----------------------------------------
\renewcommand{\baselinestretch}{1.5}
\setlength{\oddsidemargin}{0.8cm}
\setlength{\evensidemargin}{0.8cm}
\setlength{\textwidth}{14cm}
\setlength{\textheight}{23cm}
\setlength{\topmargin}{-0.8cm}
\setlength{\parindent}{0pt}
%----------------------------------------
\begin{document}
%----------------------------------------
%Redefine pagestyle {plain}
\fancypagestyle{plain}{%
%% Clear all headers and footers
\fancyhf{}
\fancyhead[LE,LO]{Thorsten Sohn, 1076041}
\fancyhead[CE,CO]{\thepage\ von \pageref{LastPage}}
}
%----------------------------------------
\pagestyle{fancy}
\renewcommand{\sectionmark}[1]{\markright{\thesection\ #1}}
\fancyhf{}
\fancyhead[LE,LO]{Thorsten Sohn, 1076041}
\fancyhead[CE,CO]{\thepage\ von \pageref{LastPage}}
%----------------------------------------
\chapter{first}
\lipsum[1-6]
%----------------------------------------
\end{document}

Since you are using koma script, it is advisable to use scrpage2 to design headers and footers. This gives almost all the benefits of fancyhdr and more flexible for use.
\documentclass[12pt, bibliography=totoc,plainheadsepline,plainheadtopline]{scrreprt}
%------------------------------------------------
\usepackage{ngerman}
\usepackage[T1]{fontenc}
\usepackage[isolatin]{inputenc}
%------------------------------------------------
\usepackage{graphicx}
\usepackage[german]{varioref}
\usepackage{moreverb}
\usepackage{lastpage,lipsum}
\usepackage{scrpage2}%<-----here
%------------------------------------------------
\renewcommand{\baselinestretch}{1.5}
\setlength{\oddsidemargin}{0.8cm}
\setlength{\evensidemargin}{0.8cm}
\setlength{\textwidth}{14cm}
\setlength{\textheight}{23cm}
\setlength{\topmargin}{-0.8cm}
\setlength{\parindent}{0pt}
%------------------------------------------------
\begin{document}
%------------------------------------------------
%% Clear all headers and footers
\clearscrheadings
\clearscrplain
\clearscrheadfoot
%------------------------------------------------
\renewcommand{\sectionmark}[1]{\markright{\thesection\ #1}}
%------------------------------------------------
\cehead[\thepage\ von \pageref{LastPage}]{\thepage\ von \pageref{LastPage}}
\cohead[\thepage\ von \pageref{LastPage}]{\thepage\ von \pageref{LastPage}}
\lehead[Thorsten Sohn, 1076041]{Thorsten Sohn, 1076041}
\lohead[Thorsten Sohn, 1076041]{Thorsten Sohn, 1076041}
\setheadwidth[0pt]{head}
\setheadtopline{2pt}
\setheadsepline{.4pt}
%------------------------------------------------
\pagestyle{scrheadings}
%------------------------------------------------
\chapter{First chapter}
\section{First section}
\lipsum[1-6]
%------------------------------------------------
\end{document}

Please refer to scrguien.pdf page number 110 chapter 4 and sections 4.1 with 4.1.1 for more details.