I checked the capacitors only with continuity test /beep test/ but now that you ask I have a feeling that its not the right way to check them … or?
Capacitor is open to DC, so continuity tester will not show anything useful apart from the possible initial blip when capacitor is charging. But for small capacitors you won't see anything.
If the meter shows that capacitor is shorted, for example, then there is a chance that it is bad. There is also a chance that it is actually across some low resistance circuit.
If you have a reason to suspect the capacitor (visual indicators), and it shows as shorted, then it makes sense to remove it and measure the PCB again. If the short goes away, then capacitor is at fault. If the short stays, then capacitor was fine.
Generally fixing laptops without a schematic is not going to lead anywhere. And even with the schematic it may not be trivial.