Buck Regulator Output is too Small
L4970A data sheet here

Your cited application note here - veryy extensive and useful.

Fig 60 circuit that you say you used is shown below.
 The circuit looks potentially OK as is.


  Frequency about 227 kHz.
   I made my inductor myself, but I'm not sure about it's characteristic.


The ability of the inductor to carry the current required without saturating is 
crucial. Can you provide a picture of the inductor and describe the core material used. At a minimum if a picture is not available please provide construction details with core material and dimensions.

What voltage does the laptop require.
 If 19V then at 1A it looks like R = V/I = 19/1 ~= 20 Ohms load and at 4A it looks like ~= 5 ohms.
 At say 10 Ohms you'd get ~= 2A.
 Power = V x I ~= 40W 

When you load it with a 10 Ohm, 40W rated resistor, what happens?
 Use an app[ropriate length of Nichrome wire (eg from an old heater or toaster element)or say 4 x 10W, 10Ohm resistors in series parallel (2S2P).