Centered with respect to the PAPER, regardless of other content on page, stealing my answer from What are the ways to position things absolutely on the page?
REVISED ANSWER
This accounts for the OP's edited purpose, namely "I want to write a letter that consists of two paragraphs, centered vertically on the page. There also has to be an address on the top, but I do not want this to influence the centering."
\documentclass{article}
\usepackage{everypage}
\usepackage{lipsum}
% THESE ARE LaTeX DEFAULTS; CAN CHANGE IF NEEDED.
\def\PageTopMargin{1in}
\def\PageLeftMargin{1in}
\newcommand\atxy[3]{%
\AddThispageHook{\smash{\hspace*{\dimexpr-\PageLeftMargin-\hoffset+#1\relax}%
\raisebox{\dimexpr\PageTopMargin+\voffset-#2\relax}{#3}}}}
% VERIFIED THAT SETTING \hoffset AND \voffset DO NOT BREAK SOLUTION.
%\hoffset=0.4in
%\voffset=0.2in
\begin{document}
\noindent Name\\
Address\\
Anytown, USA 12345
\atxy{.5\paperwidth}{.5\paperheight}{%
\makebox[0pt]{\parbox{\textwidth}{\parindent1em\relax\lipsum[1-2]}}}
\end{document}

ORIGINAL ANSWER
\documentclass{article}
\usepackage{everypage}
\usepackage{lipsum}
% THESE ARE LaTeX DEFAULTS; CAN CHANGE IF NEEDED.
\def\PageTopMargin{1in}
\def\PageLeftMargin{1in}
\newcommand\atxy[3]{%
\AddThispageHook{\smash{\hspace*{\dimexpr-\PageLeftMargin-\hoffset+#1\relax}%
\raisebox{\dimexpr\PageTopMargin+\voffset-#2\relax}{#3}}}}
% VERIFIED THAT SETTING \hoffset AND \voffset DO NOT BREAK SOLUTION.
%\hoffset=0.4in
%\voffset=0.2in
\begin{document}
\atxy{.5\paperwidth}{.5\paperheight}{%
\fboxsep=200pt\relax\makebox[0pt]{\fbox{\Huge I AM CENTERED}}}
\lipsum[1]
\end{document}

\documentclass{...}
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