My code works with arbitrary functions. I just showed it in its most simple form

fA1[w1_, w2_, w3_, w4_] := 10 + w1 + w2 + w3 + w4
fB2[r1_, r2_, r3_, r4_] := 1 + r1 + r2 + r3 + r4
fC3[t1_] := 5*t1
hF1[{fA1_, fB2_, fC3_}, {d1_, d2_, d3_, 
   d4_}] := (2*fA1[d1 + d2, d3, d1, d2])*(3*
    fB2[d1 + d2, d3, d1, d2])*(4*fC3[2*d1])

n = 100;
dom = {min, max} = {1, 10^6};
ranges = {{1, 2}, {1, 2}, {1, 2}, {1, 2}};

FindValue[{f_, fs_}, {min_, max_}, n_, ranges_] := {#, f[fs, #]} & /@ 
  Select[Transpose[RandomReal[#, n] & /@ ranges], 
   min < f[fs, #] < max &]

hF1[{fA1, fB2, fC3}, {d1, d2, d3, d4}]

FindValue[{hF1, {fA1, fB2, fC3}}, dom, n, ranges]

Or in the case the evaluation of your function takes a long time, your dont want to compute f[fs,#] twice so you can also use

FindValue2[{f_, fs_}, {min_, max_}, n_, ranges_] := 
 Block[{rand, val, sel},
  rand = Transpose[RandomReal[#, n] & /@ ranges];
  val = f[fs, #] & /@ rand;
  sel = min < # < max & /@ val;
  Pick[Thread[{rand, val}], sel, True]
  ]

Which is apparently faster even if the computation is short

FindValue[{hF1, {fA1, fB2, fC3}}, dom, n, ranges]; // AbsoluteTiming
FindValue2[{hF1, {fA1, fB2, fC3}}, dom, n, ranges]; // AbsoluteTiming

{0.0018419, Null}

{0.001193, Null}

Thanks for reviewing the code and providing your help. The problem is that the code must work for arbitrary functions.

Thank you very much for reviewing my code. Precisely, I want to use functions whose inputs will not always be like this fA1[x1 + x2, x3, x1, x2], fB2[x1 + x2, x3, x1, x2], fC3[2*x1] I've been able to get it to work by removing Module and adding Clear[x1,x2,x3,x4] to the end, but I think there must be a better way to solve it.

GT5[fA1_,fB2_,fC3_,x1_,x1min_,x1max_,x2_,x2min_,x2max_,x3_,x3min_,x3max_,x4_,x4min_,x4max_,NN_]:=
{
selectedData = {};
LowerLimit = 1;
UpperLimit = 10000000;
selectedData = {};
Do[
{
x1 = RandomReal[{x1min, x1max}];
x2 = RandomReal[{x2min, x2max}];
x3 = RandomReal[{x3min, x3max}];
x4 = RandomReal[{x4min, x4max}]; 
If[
LowerLimit <= hF1[fA1, fB2, fC3] <= UpperLimit,
selectedData = AppendTo[selectedData, {x1,x2,x3,x4,hF1[fA1, fB2, fC3]}], 
0]
}, {n, NN}
];
Print[selectedData];
Clear[x1,x2,x3,x4];
}

I want to find if the functions fA1, fB2, fC3 are within the range LowerLimit <= hF1[fA1, fB2, fC3] <= UpperLimit, using RandomReal and save the matching values into the list selectedData. But using x1,x2,x3,x4 throws error. In Module I used the relations p1=x1, p2=x2,p3=x3,p4=x4 but it does not evaluate with those assignments.

You didn't assign any values to D1, D2, etc. What were you expecting? Maybe you can explain what you're trying to achieve.