A multimeter draws next to no current, so will not effectively test the power supply under load.
The voltage on the meter is averaged out and so will not show ripple current, or spurious dips in the supply.
You will need an oscilloscope to check for ripple current (poor smoothing) and the supply needs to be under a load.
Either the supply or the multimeter is faulty.
Yes, it can be faulty. Some damaged power supplies show good output voltages on the voltage range of a multimeter but, when you connect them, they don't work properly. One possible reason is that maybe an IC in its voltage regulator has a high resistance between the common and the output. You cannot see this by shunting a voltmeter onto it. You have to place a typical load onto the output to test it.
Possible Faulty wire or even a starter or alternator failure.
Yes.
test it with a multimeter
A faulty power supply does not supply any power at all to a computer or supplies incorrect voltages. Most of the time faulty power supplies are not serviceable and require replacement.
multimeter
A dead PC could have no power going to it. The power cable could be faulty or the circuit breaker on the power supply could be flipped. If these conditions all check out, then it is likely a faulty power supply. Try these solutions. If this doesn't work, let us know ;)
Computer not booting
Either a dead battery - or a faulty power supply.
Voltage settings on the back of the power supply should be checked
Either faulty power supply or faulty wiring, the latter of which can either be hot or ground.