And some people told me that the 0.1v at the capacitor can be caused by the resistors and regulator on the board
You could listen to what "some people" told you, or you could try to figure it out for yourself.
To do this requires a very basic understanding of transformers, rectifiers, power supply filter capacitors and voltage regulator devices.
It is not all that hard, you simply have to read around the topic.
Clearly if the power supply has failed, the regulator failed, no voltage will be delivered to the pcb, or if there is an open circuit or high resistance connection, little voltage would be measured at the pcb. But also, if there is a short on the board, the voltage regulator will go into shut down mode and there will be a low voltage that way.
Generally a simple volt meter is likely all you will need. In some cases it might be helpful to measure resistance or the load current. Most meters these days are "multimeters" and will measure voltage current and resistance.
But of course to make any sense of the readings from the meter you have to understand what voltage, current and resistance are.
Voltage is an electric force field which does work on an electron current, and pushes that current around a circuit. (It is somewhat analogous to pressure which can force a flow of fluid through a pipe). In the old days it was called "electromotive force" or emf. The units of it are Joules per Coulomb (a coulomb is a large number of electrons or electric charges). Charge generally has the symbol Q. In other words this field imparts energy (joules) to the electrons.
So if one Coulomb of electrons is pushed past two terminals of a voltage source of one volt, the work done is one Joule. The work done is always Volts x Charge, or VxQ.
In electronics & electricity though, we are interested in the current or Coulombs per second, passing by some point in a circuit, we call this current I.
In any circuit, there are losses, as current flows through wires, connectors or other devices, mainly these losses occur in the circuit resistances. You can think of resistances as a device which wastes energy as heat. The units are called "Ohm's" but this is shorthand for V/I which has units of (Joules/Coulomb)/(Coulomb/second), which is Joule.Seconds/Coulomb^2
Therefore there are a set of equations which link everything together for circuits where direct currents are flowing , it is called Ohm's law, in its basic form is V=IR (voltage = current x resistance)
The power loss (heat dissipation in the resistance R) can be defined as I^2R or V^2/R, in all cases the units of power are Joules/second if you check. We call Joules per second Watts. 746 Watts is said to be one Horsepower.
Rectifier diodes for practical purposes only conduct current in one direction.
Capacitors are devices which store charge. The equation for the capacitor is Q=CV, where Q is the charge in coulombs stored in the capacitor, V is the voltage across its terminals an C is the capacitor's value in Farads. A Farad is a very large value capacitor so most of the capacitors you meet are in some number of micro-farads or uF, which is 1 millionth of a Farad.
In general, for many vintage computer power supplies, a transformer is used. Silicon rectifier diodes connected to the transformer's secondary windings, conduct on the peaks of the AC waveform to charge a large value capacitor. The voltage across the capacitor's terminals is fairly stable between peaks, but sags down a little as the capacitor discharges. This voltage is then often sent to a voltage regulator device, which maintains a stable output voltage of 5V, even if its input voltage fluctuates. Most of these voltage regulator devices, will shut down though, if their outputs get shorted out into a low Ohmic resistance, for example this could be a shorted tantalum capacitor on the pcb.
