What make and model is the laptop?
I haven't been inside a laptop power supply, but it would surprise me if it's not switchmode. Switchmode power supplies can be very tolerant of varying input voltages (for example PC power supplies often allow between 90 and 260 volts input).
19V adapters are very common for laptops. I recall a number that I've owned all having AC adapters with outputs close to that.
It is most likely that the power supply has a fault caused by something other than the input voltages.
The easiest thing to check for is swollen capacitors and charred components. Look for electrolytic capacitors with domed tops or stuff oozing out of them, or sitting at unusual angles. Look for components with charring, or parts of the board that look browned or blackened by heat.
Is the power supply a separate board from the rest of the laptop, or is it part of the motherboard?
What is your skill level?