I just added package showframe to your MWE to show you the resulting margins of your MWE.
\documentclass[english]{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{showframe} % http://www.ctan.org/pkg/showframe
\usepackage[a4paper]{geometry} % change later to \usepackage{geometry}
\geometry{verbose,tmargin=1cm,bmargin=1cm,lmargin=1cm,rmargin=1cm,headheight=0cm,headsep=0cm,footskip=0cm}
\pagestyle{empty}
\setlength{\parskip}{0bp}
\setlength{\parindent}{0pt}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{setspace}
\usepackage{babel}
\begin{document}
Text
\end{document}
To produce one page I added just "Text" as content of your document. The result is then:

Now comment the line starting with \geometry and check the result. Finaly delete the option a4paper for package geometry and compile again.
I think after that the error message is clear ;-)
On page 10 of the documentation of package geometry you find the description for 3 options to control the margins of your page. I included this options (no margins and very small, I think nearly useless? margins) in the following MWE (play with the comment signs %). You have now papersize a4 without an error message.
The new MWE:
\documentclass[english]{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{showframe} % http://www.ctan.org/pkg/showframe
\usepackage{geometry} % change later to \usepackage{geometry}
%\geometry{a4paper,verbose,tmargin=1cm,bmargin=1cm,lmargin=1cm,rmargin=1cm,headheight=0cm,headsep=0cm,footskip=0cm}
%\geometry{nomarginpar,a4paper,verbose,tmargin=1cm,bmargin=1cm,lmargin=1cm,rmargin=1cm,headheight=0cm,headsep=0cm,footskip=0cm}
\geometry{marginparwidth=0.5cm,a4paper,verbose,tmargin=1cm,bmargin=1cm,lmargin=1cm,rmargin=1cm,headheight=0cm,headsep=0cm,footskip=0cm}
\pagestyle{empty}
\setlength{\parskip}{0bp}
\setlength{\parindent}{0pt}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{setspace}
\usepackage{babel}
\begin{document}
Text
\end{document}
a4paperand\geometryare redundant, retain only one.\marginparsepand\marginparwidth. You should addnomarginparas an option togeometryif you really want those settings.\documentclass[a4paper]{report}, but\usepackage{geometry}allows you to define page layout