Insert title page into table of contents

The following seems to adhere to your request (mildly different from Guido's answer):

\documentclass[12pt,letterpaper]{report}
%for split boxes and title page
\usepackage{array}% http://ctan.org/pkg/array
%for title page
\usepackage{graphicx}% http://ctan.org/pkg/graphicx
%for double spacing in abstract
\usepackage{setspace}% http://ctan.org/pkg/setspace

\begin{document}

\pagenumbering{roman}
\thispagestyle{empty}

% --- begin title.tex

%\begin{titlepage}
\addcontentsline{toc}{chapter}{\protect\numberline{}The title of my thesis}% Add title to ToC
\begin{center}
 \vspace*{1in}
 \MakeUppercase{The Title of}\\[12pt]
 \MakeUppercase{My Thesis}\\
 % ----------------------------------------------------------------
 \vspace{1.5cm}
 by\\[12pt]
 Nathan G. Glenn\\[14pt]
  % ----------------------------------------------------------------
 \vspace{2cm}
Submitted to Brigham Young University in partial fulfillment of\\[12pt] graduation requirements for University Honors \\[5pt]

 \vfill
 % ----------------------------------------------------------------

Linguistics Department\\[12pt]
Some University\\[12pt]
{November 2012}
 \vfill

\begin{tabbing}%
   \hspace{3in}\= \kill % set up one tab position
   \centering\arraybackslash Advisor: My Advisor  \> Honors Representative: My Rep\\[12pt]
   \centering\arraybackslash Signature: \hspace{0.5cm}\makebox[1.8in]{\hrulefill} \> Signature: \hspace{0.5cm} \makebox[1.8in]{\hrulefill}
\end{tabbing}
\end{center}
%\end{titlepage}

% --- end title.tex

\clearpage

% --- begin abstract.tex

\begin{center}
\vspace*{1in}
ABSTRACT\\[36pt]
\addcontentsline{toc}{chapter}{\protect\numberline{}My abstract}% Add abstract to ToC


\MakeUppercase{The Title of}\\[12pt]
\MakeUppercase{My Thesis}\\[36pt]

Nathan G. Glenn\\[12pt]
Linguistics Department\\[12pt]
Bachelor of Arts\\[36pt]

\end{center}
\doublespacing
Is the page number arabic like it should be?

\singlespacing

% --- end abstract.tex

\clearpage

\pagenumbering{arabic}

{
\makeatletter
\let\@oldstarttoc\@starttoc
\renewcommand{\@starttoc}{%
  \addcontentsline{toc}{chapter}{\protect\numberline{}\contentsname}% Add ToC to ToC
  \@oldstarttoc
}
\tableofcontents
\makeatother
}
\chapter{Title and Abstract Should Appear Above Me in the ToC}
\chapter{Introduction}
\chapter{LitReview}
\end{document}

Instead of using the titlepage environment, I've used \pagenumbering{roman} and \thispagestyle{empty}, to remove the page numbering. For each of the title, abstract and contents, I've added a \addtocontents{toc}{chapter}{...} which sets the entry in the ToC similar to that of the chapters. This can be changed, of course.

Also, instead of loading the etoolbox package and patching \tableofcontents, a localized redefinition of \@starttoc is sufficient to add the ToC to the ToC itself.

You have to move the \pagenumbering{arabic} after \tableofcontents otherwise the page number for the abstract and the table of contents will be in arabic numerals and not roman.

Eventually, you might add a line \addtocounter{page}{1} after \end{titlepage} (titlepage resets the counter of the page at the end to 1, so the nex page after it is page 1)>

To add the title page and abstract to the content you can add the line

\addcontentsline{toc}{chapter}{<TEXT>}

somewhere in the title page file and at the beginning of the abstract file. Replace <TEXT> with whatever appropriate for the context.

For the table of contents, you can use the etoolbox package to patch it

\usepackage{etoolbox}
\patchcmd{\tableofcontents}
  {\@starttoc}
  {\addcontentsline{toc}{chapter}{\contentsname}\@starttoc}
  {}
  {}

Try this:

\documentclass[12pt,letterpaper]{report}
%for split boxes and title page
\usepackage{array}
%for title page
\usepackage{graphicx}
%for double spacing in abstract
\usepackage{setspace}

\usepackage{filecontents}

\begin{filecontents}{title.tex}
\thispagestyle{empty}
\begin{center}
 \vspace*{1in}
 \MakeUppercase{The Title of}\\[12pt]
 \MakeUppercase{My Thesis}\\
\end{center}
\end{filecontents}

\begin{filecontents}{abstract.tex}
\begin{center}
\vspace*{1in}
\chapter*{ABSTRACT}

\MakeUppercase{The Title of}\\[12pt]
\MakeUppercase{My Thesis}\\[36pt]

Nathan G. Glenn\\[12pt]
Linguistics Department\\[12pt]
Bachelor of Arts\\[36pt]
\end{center}
\doublespacing
Is the page number arabic like it should be?
\singlespacing
\end{filecontents}

\newenvironment{romanpages}
{\setcounter{page}{1}\renewcommand{\thepage}{\roman{page}}}
{\cleardoublepage\renewcommand{\thepage}{\arabic{page}}\setcounter{page}{1}}

\begin{document}

\begin{romanpages}
  \input{title}
  \addcontentsline{toc}{chapter}{Title}
  \input{abstract}
  \addcontentsline{toc}{chapter}{Abstract}
\end{romanpages}

\pagenumbering{arabic}
\setcounter{page}{1}
\tableofcontents

\chapter{Title and Abstract Should Appear Above Me in the ToC}
\chapter{Introduction}
\chapter{LitReview}
\end{document}

I have added a new environment called roman pages. Also, I have added \addcontentsline command to include title and abstract. Also, add \thispagestyle{empty} in title.tex to suppress the page number.