How to call a built function in mathematica

Your code is much too complicated. You need to break it down into simpler steps, and then try it on simpler examples, to find where the error lies.

 

In[1]:= tmp[a_, z_, w_] := Module[{m, f, d, b},
m = NDSolve[{
y1'[t] == y5[t], y2'[t] == y6[t], y3'[t] == y7[t], y4'[t] == y8[t],
y5'[t] == y9[t], y6'[t] == y10[t], y7'[t] == y11[t], y8'[t] == y12[t],
y9'[t] == y13[t], y10'[t] == y14[t], y11'[t] == y15[t], y12'[t] == y16[t],
y13'[t] == -z^4 y1[t] + 2 z^2 y9[t] + z^2 w (-t + t^2) y17[t] + a y9[t],
y14'[t] == -z^4 y2[t] + 2 z^2 y10[t] + z^2 w (-t + t^2) y18[t] + a y10[t],
y15'[t] == -z^4 y3[t] + 2 z^2 y11[t] + z^2 w (-t + t^2) y19[t] + a y11[t],
y16'[t] == -z^4 y4[t] + 2 z^2 y12[t] + z^2 w (-t + t^2) y20[t] + a y12[t],
y17'[t] == y21[t], y18'[t] == y22[t], y19'[t] == y23[t], y20'[t] == y24[t],
y21'[t] == (-1 + 2 t) y1[t] + z^2 y17[t] - a y29[t],
y22'[t] == (-1 + 2 t) y2[t] + z^2 y18[t] - a y30[t],
y23'[t] == (-1 + 2 t) y3[t] + z^2 y19[t] - a y31[t],
y24'[t] == (-1 + 2 t) y4[t] + z^2 y20[t] - a y32[t],
y25'[t] == y29[t], y26'[t] == y30[t], y27'[t] == y31[t], y28'[t] == y32[t],
y29'[t] == -y21[t] + z^2 y25[t], y30'[t] == -y22[t] + z^2 y26[t],
y31'[t] == -y23[t] + z^2 y27[t], y32'[t] == -y24[t] + z^2 y28[t],
y1[0] == y2[0] == y3[0] == y4[0] == y5[0] == y6[0] == y7[0] == y8[0] ==
y10[0] == y11[0] == y12[0] == y13[0] == y15[0] == y16[0] == y17[0] ==
y18[0] == y19[0] == y20[0] == y21[0] == y22[0] == y24[0] == y25[0] ==
y26[0] == y27[0] == y28[0] == y29[0] == y30[0] == y31[0] == 0,
y9[0] == y14[0] == y23[0] == y32[0] == 1}, {y1, y2, y3, y4, y5,
y6, y7, y8, y9, y10, y11, y12, y13, y14, y15, y16, y17, y18,
y19, y20, y21, y22, y23, y24, y25, y26, y27, y28, y29, y30, y31,
y32}, {t, 0, 1}];
f[1, 1] = y1[1] /. m;
f[1, 2] = y2[1] /. m;
f[1, 3] = y3[1] /. m;
f[1, 4] = y4[1] /. m;
f[2, 1] = y5[1] /. m;
f[2, 2] = y6[1] /. m;
f[2, 3] = y7[1] /. m;
f[2, 4] = y8[1] /. m;
f[3, 1] = y17[1] /. m;
f[3, 2] = y18[1] /. m;
f[3, 3] = y19[1] /. m;
f[3, 4] = y20[1] /. m;
f[4, 1] = y25[1] /. m;
f[4, 2] = y26[1] /. m;
f[4, 3] = y27[1] /. m;
f[4, 4] = y28[1] /. m;
d = Array[f, {4, 4}];
d = Partition[Flatten[d], 4];
b = Det[d]];
tmp[0, 3.7, 1000]

Out[2]= 15.7127

 

You will have a lot less trouble trying to write Mathematica if you understand how to use and not use the _ in your code.

This might help.
http://reference.wolfram.com/mathematica/tutorial/DefiningFunctions.html

This
Plot[tmp[0, 3.7, w], {w, 1000, 100000}]
shows how your function behaves.

But this
FindRoot[tmp[0, 3.7, w] == 0, {w, 95000, 90000, 100000}]
fails for some reason I haven't been able to isolate in your code.

This
Plot[tmp[0, 3.7, w], {w, 90000, 95000}]
can give you a good estimate.