To solve this problem you have to do several things.
First prepare your code to be compilable:
\documentclass{article}
\usepackage[%
% pdftex % be carefull!!: with this option: 2 errors, without: 0 errors
]{graphicx} % for \includegraphics
\usepackage{epstopdf} % to change .eps to .pdf
\epstopdfsetup{update} % conversion only if no .pdf file already created
\begin{document}
Now you should see the picture in pdf:
\includegraphics[width={\textwidth}]{example-image-a.eps}
\end{document}
In line 5 of the mwe I added \usepackage{epstopdf} to prepare the possibility to change .eps images to .pdf images. Line 6 starts epstopdf only, if the changed "epstopdf" file does not exist. (Please see documentation with texdoc epstopdf). Because you gave no MWE I can only guess what you are doing, here just a remark. In the epstopdf documentation is showed to call package graphicx with option pdftex. That causes in 2 errors. Without the option the code compiles with only one warning, but wanted document!
Second you have to prepare TeXnicCenter to be able to do what you want.
Prepare a new output profile, for example LaTeXshellescape=>PS=>PDF.
Copy the original LaTeX=>PS=>PDF to the new profile, and do the following changes:
- Add
-shell-escape in arguments for the compiler (see red marking):

Please see, that I changed "%bm" to "%tm" (see red markings).
- Open register
Nachbearbeitung (sorry, do not know the english name, it is the third one, see image) and check if you see:

With theese changes you will get the following compiled result without errors:

Alternative method with dvipdfmx
You can also use an alternative method with dvipdfmx (see Project KTug.org or CTAN:dvipdfmx). But then you use the way from .dvi to .pdf!
MiKTeX is not able to run several script, because Windows has no installed perl or ... interpreter. But you can use the program dvipdfmx.exe (see windows directory C:\Program Files\MiKTeX 2.9\miktex\bin\x64) to get the same result. Use dvipdfmx --help to see all possible options. I need none of them for the example here.
With the following MWE (please see that epstopdf is missing)
\documentclass{article}
\usepackage{graphicx} % for \includegraphics
\begin{document}
Now you should see the picture in pdf:
\includegraphics[width={\textwidth}]{example-image-a.eps}
\end{document}
and the following configuration (profile LaTeXdvipdfmx) for TeXnicCenter you get the wanted result.
Copy LaTeX=>DVI=>PDF to LaTeXdvipdfmx, do not add -shell-escape, change %bm to %tm (see red markings).
Now click on Nachbearbeitung and change there dvipdfm to dvipdfmx to call program dvipdfmx.exe.

Click ok and compile the mwe. The result is the same I showed above ...
dviandpsis missing/broken. If all you want is apdfoutput and you have no other reasons to go viadvi, considerpdflatexas a single step, rather than the long sequence you're using. – greyshade Aug 13 '14 at 10:42-shell-escapewhen invokingpdflatex. i.e. in TeXnicCenter where the commands for the compilation options are defined in the settings, add-shell-escapebefore the filename – greyshade Aug 13 '14 at 11:37pdflatex- I don't have TeXnicCenter here atm. – greyshade Aug 13 '14 at 11:54-interaction=nonstopmode -shell-escape "%pm". – greyshade Aug 13 '14 at 12:27(epstopdf). oh, and you did add\usepackage{epstopdf}to the preamble as suggested in the links in my second comment? – greyshade Aug 13 '14 at 12:40