Problem with the table of contents indentation/spacing

I must admit that I am not fond of your institution's template, whatever that might be. Try the following and see if it produces what you are after.

% thesistocprob.tex  SE 581226

makeatletter
letmy@xfloat@xfloat
makeatother

documentclass[oneside,12pt,a4paper]{book}
%documentclass[12pt,a4paper]{book}

usepackage{comment}

%usepackage{UTMThesis, enumerate, amsfonts, longtable, qtree, etoolbox, array, rotating, pgf, tikz, tikz-cd, algorithm, csquotes}

makeatletter
def@xfloat#1[#2]{
    my@xfloat#1[#2]%
    defbaselinestretch{1}%
    @normalsize normalsize
}
makeatother

begin{comment}
allowdisplaybreaks
usetikzlibrary{arrows, matrix, positioning, shapes, shapes.geometric, calc, intersections, decorations.pathreplacing}
newcommand{tikznode}[2]{relax
    ifmmode%
    tikz[remember picture,baseline=(#1.base),inner sep=0pt] node (#1) {$#2$};
    else
    tikz[remember picture,baseline=(#1.base),inner sep=0pt] node (#1) {#2};%
    fi}
letopenboxrelax
letiintrelax
letiiintrelax
letiiiintrelax
letidotsintrelax
end{comment}

newcommand*{qed}{hfillensuremath{square}}

%-------------------------------------------------------------
usepackage{cite}                       % change  cite from [1,2,3] to [1-3] etc for number system
makeatletter                           % change from
  renewcommand{@biblabel}[1]{#1.}     % [1] to 1. etc 
makeatother                            % in list of references
%-----------------------------------------------------------
  setlength{voffset}{-2.1cm}
  setlength{hoffset}{-.4cm}  
%--------------------------------------------------------
fontfiverm=cmr5 
%input{Pictex.tex} % using pictex
%---------------------------------------------------------
%pagestyle{plain}
%-------------------------------------------------------
  usepackage{fancyhdr}
  pagestyle{fancy}
  lhead{}
  chead{}
  rhead{}
  lfoot{}  
  cfoot{vspace{-.35cm}thepage}  % 
  rfoot{} 
  renewcommand{headrulewidth}{0pt}
%-------------------------------------------------------

usepackage{tocloft}
renewcommand{cftchappresnum}{textbf{CHAPTER }}
setlength{cftchapnumwidth}{3cm}
renewcommand{contentsname}{TABLE OF CONTENTS}

begin{document}
frontmatter

addtocontents{toc}{textbf{CHAPTER} hfill textbf{TITLE} hfill textbf{PAGE} par}
%chapter*{TABLE OF CONTENTS}
addcontentsline{toc}{section}{contentsname}
tableofcontents

begin{comment}
addcontentsline{toc}{section}{textbf{TABLE OF CONTENTS}}
contentsline{toc}{hspace{-1.3cm}phantom{textbf{CHAPTER}}hfill
    textbf{TITLE}hspace{1.1cm}}hfill {textbf{PAGE,,}}
end{comment}

setlength{parskip}{.25cm}
    setlength{baselineskip}{.5cm}
begin{comment}    
%    contentsline {chapter}{numberline {hspace {-.9cm}CHAPTER 1}hspace{1cm}THIS IS A VERY LONG LONG LONG LONG LONG LONG TITLE}{1}
    contentsline {chapter}{numberline {CHAPTER 1}hspace{2.5cm}THIS IS A VERY LONG LONG LONG LONG LONG LONG TITLE}{1}
    contentsline {section}{numberline {hspace {-.175in}1.1hspace {.12in}}Background Problem}{1}
end{comment}
mainmatter

chapter{THIS IS A VERY LONG LONG LONG LONG LONG LONG TITLE}
section{Background Problem}

backmatter
end{document}

It is a heavily revised version of your MWE but generally abides by the usual LaTeX style. It uses the regular LaTeX chapter, unlike your MWE, but uses the tocloft package to get the ToC as I think that your template wants.