General unstability for a PSU with improper curent filtering or inadequate tentions. First step: replace the power strip as it may be faulty and cause current noise. If replacing the power strip bring no change, the PSU is faulty.
Total failure to power up: The PSU is dead and need to be replaced. (may also be a faulty power switch connection, a disconnected power line, a bad power strip or the switch of the power strip been in the OFF position)
Failure of some components meaning that some, but not all, power cables don't get proper alimentation. This may show up as a specific hard drive or any other device not working. May be circumvented by using another available connector.
Place your hand near the PSU air vent. You should feel some warm air flow. No warm air flow = non-working PSU fan leading it to overheat. It can lead to fire hasard.
In all cases, it's needed, or at least recomended, to replace the PSU by one of similar, or slightly higher, power rating.