push(my @file2, $_);
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Since you didn't post all of your code, I'm not 100% certain how you're doing your scoping, but I bet the my keyword there is why your @file2 is appearing empty or nearly so below. It will scope @file2 within that block (the if block, most likely).

my @file2;             # scope it OUTSIDE of your block
while (<FILE2>) {
   if (s/.../.../) {
      push(@file2, $_);
   }
}   # end your while here??

# ...

print FILE3, @file2;   # prints all elements
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