The function is

function ReadMWord(f: TFileStream): Word;
type
  TMotorolaWord = record
    case Byte of
      0: (Value: Word);
      1: (Byte1, Byte2: Byte);
  end;
var
  MW: TMotorolaWord;
begin
  f.read(MW.Byte2, SizeOf(Byte));
  f.read(MW.Byte1, SizeOf(Byte));
  Result := MW.Value;
end;

procedure GetPNGSize(const sFile: string; var wWidth, wHeight: Word);
type
  TPNGSig = array[0..7] of Byte;
const
  ValidSig: TPNGSig = (137,80,78,71,13,10,26,10);
var
  Sig: TPNGSig;
  f: tFileStream;
  x: integer;
begin
  FillChar(Sig, SizeOf(Sig), #0);
  f := TFileStream.Create(sFile, fmOpenRead);
  try
    f.read(Sig[0], SizeOf(Sig));
    for x := Low(Sig) to High(Sig) do
      if Sig[x] <> ValidSig[x] then Exit;
    f.Seek(18, 0);
    wWidth := ReadMWord(f);
    f.Seek(22, 0);
    wHeight := ReadMWord(f);
  finally
    f.Free;
  end;
end;

Example usage:

var width,height:word;
begin
  GetPNGSize(filename,width, height);
end;