What you need is a Digital Volt Meter (DVM for short).
If you looking at the different parts of the PCB, such as a motherboard. Denote, where the 3.3 volts, 5 volts and other voltages come in, these are known as rails on the motherboard, as in power supply rails.
What I need to know is. What kind of capacitors are you attempting to test, DC or AC based capacitors? The DC capacitors on the motherboard for stabilizing the power supply across the rails on the motherboard are DC type. The filter capacitors, to knock out noise from crosstalk and other sources of noise aren't polarized. Slightly different test methods for each is employed.
From a straight electrical standpoint, if you want to test for open circuits, leaky capacitors or short circuits.
First look at all your capacitor tops and side to make sure they're flat on the top, meaning not bulging. If they're bulging, you have a bad capacitor, one of two things happened open circuit or leaky capacitor (meaning capacitor can't hold on to it's rated charge for x amount of time at said voltage).
Look for stuff that looks like dried cola on the motherboard surrounding your capacitors, some capacitors are solid some still have liquid electrolytic solution, it turns brown to black after it leaks out and oxidizes.
Some electrolytes in these capacitors are corrosive and care should be taken to clean it up, using denatured ethyl alcohol to dissolve that mess is the best bet, do all of this when the power is off and have unplugged the unit from the power supply. That you cycled the power button from the case so that all remaining power in the capacitors and other components discharge before you attempt to do this.
Take a look at this convenient link on how to identify and test capacitors if you suspect they may be bad.
"This could be due the fact that more data is getting transferred and therefore more data is getting corrupted by the noise or it could be due to the SMPSs working harder to power the GPU resulting in more noise."
The noise you are getting is bursty in nature, that will happen when multiple lines of analog communications in this case video signals begin to be transmitted.
Whether you know it or not, the PCI-E bus line actually uses diffential analog signalling which can wreak havoc on digital system that aren't properly filtering out the noise or the digital ground plane may be broken in on or more areas on the board. Could be that the analog ground could also have some of those problems too.
Analog and digital grounds are different and don't meet on the motherboard, except through diodes to chassis or earth grounds.
I said that the video also has analog signaling. Most motherboard chipsets have an analog port on them, whether or not their used in the design, is something else. For those who have a VGA port or a DVI-I connector, which carries both
analog (VGA compatible line level signals) and digital DVI signals in the same
connector can be a concern.
Video in general, even if having a digital video signal (less bandwidth needed than analog at the same resolution and color depth), has a fairly wide bandwidth and can raise hell trying to find the problem.
When testing motherboards, always unplug all accessory cards from the system, if you have on-board video enable it but get into the BIOS note all the settings, including RAM timing. Then set it to default, then test again.
Some of the noise you are getting may or may not be the motherboard at all, it could be on the accessory cards or be an overburdened power supply causing all those crazy problems. Most people don't get the correct PSU for their computers and then add in a power hungry graphics card that after awhile slow starts to destroy your PSU, then you start to see caps pop (go bad), hear weird noises coming from your system. Start to see weird artifacts on the screen or the system just crashes out of the blue.
Now, here is the trick, if it has to do with layers in your motherboard, signal, grounds, different power planes 5 volt, 3.3 volt, it might not be worth it to try to fix.
It's one thing if it's just the signal layers on top you can fix with circuit tape and soldering but if it the planes inside the layered motherboard, there is no way to tell how long that will last.
You would need some pretty expensive hardware to see the faults in the motherboard to see if the other layers are faulty anywhere else. You will need a specialized x-ray inspection machine meant for First Article Inspection and a unit that high end technician and engineers use. Traditionally, First Article Inspection is looking for dead head components (tombstones) open circuits, etc.
Although, some do use x-ray machines to look for faults if a test technician notices a group of circuits from a given panel or set of motherboards aren't working once they've been fully populated (all the components put on correctly).
I've used these machines in the past and you need to be specially trained on how to use them and go through special safety procedures too. They look similar to a pick and place machine used in assembly of PCB but taller and longer, they also use CNC style commands with option of using Gerber files over a network adapter to scan as an automated unit.
I realize some of this may be way over your head and I would like to apologize for that. Trying to fix motherboards with no basic electronics skill, this is a recipe for disaster.