Also I don't know what effect writing a text file has after you read the line, are you trying to duplicate the lines of the file? Try commenting out your WriteLn() call and doing something else with the read-in string.
procedure TForm1.Button4Click(Sender: TObject);
fName, fOut: String;
fName := 'C:\test.txt';
while not eof(FileA) do
The above code will write the entire contents of a file, line by line, out to the command prompt. If you are not using the output type as a console application it will generate I/O error 105.