Don't forget to take a look at the car battery itself. When the terminals become corroded, they can provide enough resistance to prevent the high current needed for starting while still allowing for sufficient current for most of the normal electrical loads.
Also, on the first attempt to start, the high current requested can heat the corrosion site enough to break down the insulating characteristics so that, on the second attempt to start, there is less resistance thus allowing sufficient current to pass.
It is not too hard to remove the battery container cover. Press the finger latch at the back on the right and then on the left while pulling up on the back of the cover. Look at the negative terminal for corrosion. Then, lift the cover over the positive terminal to look for corrosion there.