Power surges are a bit tricky and there is no real way to absolutely know what may have been damaged by the surge. Generally, the surge protector is your 1st defense against a power surge. Not all protectors are the same some offer more protection than others (larger surges).
The next line of defense is the power supply. Assuming the power surge is not excessive, the PSU may actually survive intact. If it gets overwhelmed, then the PSU can be damaged. If the PSU is of poor quality and / or the power surge is excessive, then the power surge can actually completely destroy every single component. That would be the worse possible scenario.
Generally, there are no physical signs of electrically damaged components except for maybe a blown capacitor. Therefore, each component must be tested individually. Hopefully, it is just the PSU that is the problem. If you or a friend have a spare PSU then you can use that to see if the PC will boot up.
Do not attach your damaged PSU in another PC.