Can I make an entire listing a hyperlink rather than just the code?

This might do the trick - but - no warranties! ;-)

documentclass{article}

usepackage{listings}
usepackage[colorlinks=true]{hyperref}
%usepackage[colorlinks=false]{hyperref}

makeatletter
newsaveboxnewglowscriptblockTempBox
newcommandnewglowscriptblockURL{}%
newcommandnewglowscriptblockWrapInPartopsep[1]{%
   vskippartopsep#1vskippartopsep
}%
lstnewenvironment{newglowscriptblock}[3]{%
  gdefnewglowscriptblockURL{#3}%
  setboxnewglowscriptblockTempBoxhbox{begingroupaftergroup}%
  lstset{caption={#1},label={#2}}%
}{%
  endgroup
  hypersetup{hidelinks}%
  ifvmodeendgrafexpandafternewglowscriptblockWrapInPartopsepelseendgrafexpandafter@firstofonefi
  {%
    vskiptopsep
    noindent
    expandafterhrefexpandafter{newglowscriptblockURL}{usebox{newglowscriptblockTempBox}}%
    endgraf
    vskiptopsep
  }%
}%
% Make sure hyperref's href gets its argument "normalized
@ifdefinablenewglowscriptblock@@{%
  letnewglowscriptblock@@=newglowscriptblock@
  renewcommandnewglowscriptblock@[2]{hyper@normalise{newglowscriptblock@@unexpanded{{#1}{#2}}}}%
}%
makeatother


begin{document}

lstlistoflistings

newpage

Some text. Some text.
Some text. Some text.
begin{newglowscriptblock}{Problem 37 Code}{pref2}{https://google.com}
GlowScript 3.0 VPython

# a Young's modulus problem

Lo = 3   # wire's original length in m
d = 3e-3 # wire's diameter in m
g = 9.8  # surface grav. field strength in N/kg
m = 10   # ball's mass in kg
Y = 2e11 # steel's Young's modulus in N/m^2
# Find DeltaL, the amount the wire stretches.

area = (pi*d**2)/4
Force = m*g
DeltaL = (Force*Lo)/(area*Y)

print ("The wire stretches by ",DeltaL," m")
end{newglowscriptblock}
Some text. Some text.
Some text. Some text.

newpage

nameref-link to listing: nameref{pref2}

ref-link to listing: ref{pref2}

pageref-link to listing: pageref{pref2}

autoref-link to listing: autoref{pref2}

end{document}

---

Addendum in October 21, 2020

In a comment from October 20, 2020 you asked:

If I don't want to supply a URL, is there a way to suppress hyperref's warning about an empty target OR can I supply something that won't make the code highlight if I click it with the mouse?

The pdf-viewer used by me doesn't highlight things when clicking with the mouse. I assume the highlighting is not due to the pdf-file but is a feature "hardwired" in your pdf-viewing program.

If you don't mind changing the order of the arguments of the environment so that the argument holding the URL will not be the third one but will be the first one, you can make that argument optional, with an empty default.

You need to do some trickery to have the URL-argument normalized for hyperref. Otherwise you cannot have characters like # within the URL.

Then you can add forking to check whether the expansion of the macro newglowscriptblockURL defined from the URL-argument yields "blankness", i.e., emptiness or explicit space tokens only, and apply href only if this is not the case. This way if the now optional URL-argument is not provided or is provided empty, attempts at creating a hyperlink will not take place:

documentclass{article}

usepackage{listings}
usepackage[colorlinks=true]{hyperref}
%usepackage[colorlinks=false]{hyperref}

makeatletter

% Infrastructure for "hyperref-normalizing" an optional argument of a lstnewenvironment:
begingroup
catcode`^^A=14 %
catcode`^^Mactive^^A
catcode`%active^^A
@ifdefinablehyper@@normaliseoptarg{^^A
  gdefhyper@@normaliseoptarg#1#2#3]{^^A
    edefHy@tempa{^^A
      endgroupnoexpand#1[{Hy@RemovePercentCr#3%^^M@nil}]^^A
    }^^A
    Hy@tempa^^A
  }^^A
}^^A
endgroup
newcommandMY@exchange[2]{#2#1}%
expandafternewcommandexpandafter*expandafterhyper@normaliseoptargexpandafter{%
  romannumeral0%
  expandafterMY@exchangeexpandafter{hyper@normalise}{%
    @firstofone{expandafter} %
    MY@exchange{lethyper@@normalise=hyper@@normaliseoptarg}%
  }%
}%
newcommandlstenv@testhyper@normalizeopt[2]{%
  @ifnextchar[{catcode active 5relaxhyper@normaliseoptarg{lstenv@testoptnoexpand#1{#2}}}%
               {hyper@normaliseoptarg{#1}[{#2}]}%
}%
% end of Infrastructure for "hyperref-normalizing" an optional argument of a lstnewenvironment.


newsaveboxnewglowscriptblockTempBox
newcommandnewglowscriptblockURL{}%
newcommandnewglowscriptblockWrapInPartopsep[1]{%
   vskippartopsep#1vskippartopsep
}%
lstnewenvironment{newglowscriptblock}[3][]{%
  gdefnewglowscriptblockURL{#1}%
  setboxnewglowscriptblockTempBoxhbox{begingroupaftergroup}%
  lstset{caption={#2},label={#3}}%
}{%
  endgroup
  ifxnewglowscriptblockURLemptyelsehypersetup{hidelinks}fi
  ifvmodeendgrafexpandafternewglowscriptblockWrapInPartopsepelseendgrafexpandafter@firstofonefi
  {%
    vskiptopsep
    noindent
    ifcat $detokenizeexpandafterexpandafterexpandafter{expandafter@firstoftwonewglowscriptblockURL{}.}$%
    expandafter@firstoftwoelseexpandafter@secondoftwofi
    {@firstofone}%
    {expandafterhrefexpandafter{newglowscriptblockURL}}%
    {usebox{newglowscriptblockTempBox}}%
    endgraf
    vskiptopsep
  }%
}%
% Make sure hyperref's href gets its argument "hyperref-normalized" by replacing
% lstenv@testopt with lstenv@testhyper@normalizeopt
% in the definition of newglowscriptblock@.
expandafterrenewcommandexpandafter*expandafternewglowscriptblock@expandafter{%
  romannumeral0%
  expandafterMY@exchangeexpandafter{%
    csnamestringnewglowscriptblock@endcsname{}%<-the default for the opt arg is between these braces. The default is empty.
  }{ %
    ifxprotect@typeset@protect
      expandafterlstenv@testhyper@normalizeopt
    else
      @x@protectnewglowscriptblock@ 
    fi
  }%
}%
makeatother

begin{document}

lstlistoflistings

newpage

Some text. Some text.
Some text. Some text.
The optional argument is not empty, thus the environment is a hyperlink. %
begin{newglowscriptblock}[https://google.com#Weird]{Problem 37 Code}{pref2}
GlowScript 3.0 VPython

# a Young's modulus problem

Lo = 3   # wire's original length in m
d = 3e-3 # wire's diameter in m
g = 9.8  # surface grav. field strength in N/kg
m = 10   # ball's mass in kg
Y = 2e11 # steel's Young's modulus in N/m^2
# Find DeltaL, the amount the wire stretches.

area = (pi*d**2)/4
Force = m*g
DeltaL = (Force*Lo)/(area*Y)

print ("The wire stretches by ",DeltaL," m")
end{newglowscriptblock}
The optional argument is not empty, thus the environment is a hyperlink.
Some text. Some text.
Some text. Some text.

newpage

Some text. Some text.
Some text. Some text.
The optional argument is empty, thus the environment is not a hyperlink.
begin{newglowscriptblock}{Problem 37 Code}{pref3}
GlowScript 3.0 VPython

# a Young's modulus problem

Lo = 3   # wire's original length in m
d = 3e-3 # wire's diameter in m
g = 9.8  # surface grav. field strength in N/kg
m = 10   # ball's mass in kg
Y = 2e11 # steel's Young's modulus in N/m^2
# Find DeltaL, the amount the wire stretches.

area = (pi*d**2)/4
Force = m*g
DeltaL = (Force*Lo)/(area*Y)

print ("The wire stretches by ",DeltaL," m")
end{newglowscriptblock}
The optional argument is empty, thus the environment is not a hyperlink.
Some text. Some text.
Some text. Some text.

newpage

nameref-link to listing pref2: nameref{pref2}

ref-link to listing pref2: ref{pref2}

pageref-link to listing pref2: pageref{pref2}

autoref-link to listing pref2: autoref{pref2}

nameref-link to listing pref3: nameref{pref3}

ref-link to listing pref3: ref{pref3}

pageref-link to listing pref3: pageref{pref3}

autoref-link to listing pref3: autoref{pref3}

end{document}