No way to really know.
Determining what specifically went "bang" might provide some insight.
Electricity travels very fast and will follow any path it can get any especially the literal path of least resistance.
If the damage is/was restricted to just the PSU then the computer may have survived completely. Or maybe just had a couple of components damaged.
Damage may or may not be visible.
No harm in unplugging the computer and inspecting everything inside with a bright flashlight. Look for signs of melting, bare conductor showing, black/brown streaks , burn marks, swollen components, etc..
As for truly working (aka "alright") you will need to breadboard each component in another known working computer. Which entails some risk to that computer if the component being tested is damaged in a manner to cause a domino effect.
Pull the drives and at least get your data backed up before doing anything.