How do I join the vertical lines here in the table?

Here are three different examples showing how to...

1. make your code compilable,
2. get rid of the gaps in the vertical lines
3. fit your table into the available space without using adjustbox
4. improve the alignment of numbers inside of the table.

In the first two examples, I have removed adjustbox and instead used a landscape page for the wide table, while I entirely changed the table layout in the third example. In the second and third example, I have removed all vertical lines and replaced the horizontal ones by rules from the booktabs package. Additionally, I used the siunitx package in order to improve the alignment of the numbers:

documentclass[letterpaper]{article} % DO NOT CHANGE THIS
usepackage{times}  % DO NOT CHANGE THIS
usepackage{helvet} % DO NOT CHANGE THIS
usepackage{courier}  % DO NOT CHANGE THIS
usepackage[hyphens]{url}  % DO NOT CHANGE THIS
usepackage{graphicx} % DO NOT CHANGE THIS
urlstyle{rm} % DO NOT CHANGE THIS
defUrlFont{rm}  % DO NOT CHANGE THIS
usepackage{graphicx}  % DO NOT CHANGE THIS
usepackage{natbib}  % DO NOT CHANGE THIS AND DO NOT ADD ANY OPTIONS TO IT
usepackage{caption} % DO NOT CHANGE THIS AND DO NOT ADD ANY OPTIONS TO IT
usepackage{multirow}
usepackage{makecell}
usepackage{adjustbox}
usepackage{amsmath}
usepackage{bm}
usepackage{amssymb}
usepackage{mathtools}
usepackage{textcomp}
usepackage{array}
usepackage{pbox}
frenchspacing  % DO NOT CHANGE THIS
setlength{pdfpagewidth}{8.5in}  % DO NOT CHANGE THIS
setlength{pdfpageheight}{11in}  % DO NOT CHANGE THIS

usepackage{pdflscape}
usepackage{booktabs}
usepackage{siunitx}
begin{document}
begin{landscape}
begin{table}
centering
begin{tabular}{c|c|cc|cc|cc|c}
hline
multirow{3}{*}{Network}  & multirow{3}{*}{makecell{Score Type}} & multicolumn{2}{c|}{multirow{3}{*}{High SNR}} & 
multicolumn{2}{c|}{multirow{2}{*}{Medium SNR}} &
multicolumn{2}{c|}{multirow{2}{*}{Low SNR}} &
multirow{3}{*}{makecell{Timeper epoch(secs)}} 
& & & & &  &  &  &     
& & MAE & PE (%) & MAE & PE(%) & MAE & PE(%) & hline hline 

multirow{2}{*}{SVR} 
& R & 8.89$pm$2.07 & 100$pm$0.00 &  9.23$pm$1.85 & 100$pm$0.00 &  9.70$pm$1.38 & 100$pm$0.00 & multirow{2}{*}{---}  
& E & 9.97$pm$2.45 & 96.29$pm$8.30 & 10.08$pm$2.46 & 96.28$pm$8.32 & 10.31$pm$1.56 & 96.40$pm$8.05 &      hline 
multirow{2}{*}{Lasso}                                                         
& R & 18.57$pm$5.28 & 44.89$pm$21.06 & 18.56$pm$5.28 & 44.84$pm$21.12 & 18.55$pm$5.24 & 44.85$pm$21.02 & multirow{2}{*}{---} 
& E & 18.60$pm$3.58 & 43.19$pm$8.66 &  18.60$pm$3.57 & 42.95$pm$8.50 &  18.61$pm$3.56 & 43.01$pm$8.61  &      hline 
end{tabular}
caption{....}
label{table:tab2}
end{table}
end{landscape}

begin{landscape}
begin{table}
centering
sisetup{separate-uncertainty=true}
setlength{tabcolsep}{5.5pt}
begin{tabular}{l l *{3}{S[table-format=2.2(3)]S[table-format=3.2(4)]} c}
toprule
Network  
  & makecell{Score Type} 
    & multicolumn{2}{c}{High SNR} 
      & multicolumn{2}{c}{Medium SNR} 
        & multicolumn{2}{c}{Low SNR} 
          & makecell{Timeper epoch(secs)} 
cmidrule(r){3-4} cmidrule(lr){5-6} cmidrule(l){7-8}
&   & {MAE}      & {PE (%)}   & {MAE}      & {PE(%)}    & {MAE}      & {PE(%)}   & 
midrule
SVR 
& R & 8.89(207)  & 100(0)      &  9.23(185) & 100(0)      &  9.70(138) & 100(0)     & ---  
& E & 9.97(245)  & 96.29(830)  & 10.08(246) & 96.28(832)  & 10.31(156) & 96.40(805) & --- 
midrule 
Lasso                                                        
& R & 18.57(528) & 44.89(2106) & 18.56(528) & 44.84(2112) & 18.55(524) & 44.85(2102) & --- 
& E & 18.60(358) & 43.19(866)  & 18.60(357) & 42.95(850)  &  18.61(356) & 43.01(861) & ---  
bottomrule 
end{tabular}
caption{....}
label{table:tab2}
end{table}
end{landscape}


begin{table}
centering
sisetup{separate-uncertainty=true}
setlength{tabcolsep}{5.5pt}
begin{tabular}{l l S[table-format=2.2(3)]S[table-format=3.2(4)] c}
toprule
Network 
  & multirow{2}{*}{makecell{Score Type}}
    & multicolumn{2}{c}{High SNR}
          & multirow{2}{*}{makecell{Time per epoch (secs)}} 
cmidrule(r){3-4} 
&   & {MAE}      & {PE (%)}    
midrule
SVR 
& R & 8.89(207)  & 100(0)       & ---  
& E & 9.97(245)  & 96.29(830)   & --- 
addlinespace
Lasso                                                        
& R & 18.57(528) & 44.89(2106)  & --- 
& E & 18.60(358) & 43.19(866)   & ---  
midrule
Network 
  & multirow{2}{*}{makecell{Score Type}}
    & multicolumn{2}{c}{Medium SNR}
          & multirow{2}{*}{makecell{Time per epoch (secs)}} 
cmidrule(r){3-4} 
&   & {MAE}      & {PE (%)}    
midrule
SVR 
& R  &  9.23(185) & 100(0)      & ---  
& E  & 10.08(246) & 96.28(832)  & --- 
addlinespace
Lass                            
& R  & 18.56(528) & 44.84(2112)  & --- 
& E  & 18.60(357) & 42.95(850)   & ---  
midrule
Network 
  & multirow{2}{*}{makecell{Score Type}}
    & multicolumn{2}{c}{Low SNR}
          & multirow{2}{*}{makecell{Time per epoch (secs)}} 
cmidrule(r){3-4} 
&   & {MAE}      & {PE (%)}    
midrule
SVR 
& R  &  9.70(138) & 100(0)     & ---  
& E  & 10.31(156) & 96.40(805) & --- 
addlinespace
Lass    
& R  & 18.55(524) & 44.85(2102) & --- 
& E  &  18.61(356) & 43.01(861) & ---  
midrule
end{tabular}
caption{....}
label{table:tab2}
end{table}
end{document}

You haven't indicated how wide your document's margins are. Assuming they're about 1" wide each, it's actually possible to typeset the table in portrait mode without having to resort to the adjustbox cudgel.

Since your document employs the times text font package, I would like to strongly encourage you to use a Times Roman math font package; one such package is newtxmath.

I would also like to encourage you to give a table a much more open "look", mainly by getting rid of all vertical rules and by using fewer, but well-spaced, horizontal rules by using the line-drawing macros of the booktabs package.

---

Just to demonstrate the most unfortunate effects that using adjustbox can have on tables, here's a screenshot of the table that's produced by your original code. Note, in particular, the wild disparity in font sizes of the body of the table on the one hand and of the caption on the other.

---

Finally, here's the code that produced the first screenshot.

documentclass[letterpaper]{article}
usepackage{amsmath,booktabs,multirow,makecell}
usepackage[margin=1in]{geometry} % set margins as needed
usepackage{times,newtxmath} % use a Times Roman math font
usepackage{array}
newcolumntype{C}{>{$}c<{$}}
newcommandx[1][1]{phantom{#1}} % for spacing adjustments
newcommandpx{mathord{pm}} % "pm" but without the spacing
begin{document}
begin{table}[ht]
setlengthtabcolsep{0pt}## Heading ##
begin{tabular*}{textwidth}{@{extracolsep{fill}} 
           l c *{6}{C} c }
toprule
Network 
  & makecell{ScoreType} 
  & multicolumn{2}{c}{High SNR} 
  & multicolumn{2}{c}{Medium SNR} 
  & multicolumn{2}{c}{Low SNR} 
  & makecell{Timeper epoch} 
cmidrule{3-4} cmidrule{5-6} cmidrule{7-8}
& & text{MAE} & text{PE (%)} 
  & text{MAE} & text{PE (%)} 
  & text{MAE} & text{PE (%)}  
  & (secs) 
midrule

multirow{2}{*}{SVR} 
& R & x8.89px2.07      & x[1.]100pxx0.00 & x9.23px1.85 
    & x[1.]100pxx0.00 & x9.70px1.38      & x[1.]100pxx0.00 
    & multirow{2}{*}{--}  
& E & x9.97px2.45      & 96.29pxx8.30     & 10.08px2.46 
    & 96.28pxx8.32     & 10.31px1.56       & 96.40pxx8.05 &  
addlinespace
multirow{2}{*}{Lasso}                                                         
& R & 18.57px5.28       & 44.89px21.06      & 18.56px5.28 
    & 44.84px21.12      & 18.55px5.24       & 44.85px21.02 
    & multirow{2}{*}{--} 
& E & 18.60px3.58       & 43.19pxx8.66     &  18.60px3.57 
    & 42.95pxx8.50     &  18.61px3.56      & 43.01pxx8.61 &  
bottomrule
end{tabular*} 
caption{dots}
label{table:tab2}
end{table}
end{document}