How much power the system is REALLY consuming?
Solution 1:
The information reported by various sensors on modern CPUs, motherboards and graphics cards can be viewed with programs like CPUID's HWMonitor.
Solution 2:
I think you don't quite understand the terms you are using or the physics involved.
"Is there a way to see (in real time) how much power the whole system is trying to consume and how much is it really getting?"
Think of the power supply like a water supply line. Think of the voltage like pressure. If the pressure in the water supply line is correct, then your house is getting precisely as much water as it is trying to consume. If your house tries to draw more water than the supply can provide, the pressure will have to drop.
Maybe, not in watts, but the voltage is not enough, say, 4.5V instead of 5V.
Why is the voltage not enough? The power supply's job is to provide the right voltage, just like the water supply's job is to provide the right pressure.
What I really need to know, is should I return the power supply to a shop and buy another one.
What's the make and model of the power supply? We can tell you whether it's a decent unit or a piece of junk. You can't measure that, just like there's nothing you can measure on a car to tell you if it's well made.
Solution 3:
You could presumably work it out with a power supply tester to see if the rails output the voltage they are supposed to.
If you wanted an absolutely accurate realtime way of doing it while the system is running, it would be hugely complicated and involve monitoring each and every power lead's voltage and current, or at the very least, to do so per rail
Solution 4:
What you need is something between your PSU and wall socket.
Try something like this: http://www.velleman.eu/products/view/?id=378012
It will give you the amount of Watts used by your system. You can't have a value of what your system "needs" in terms of power. There are no signals like "I need more power" passed anywhere. You can watch the voltage on different PSU lines to see if there's something wrong going on, but looking at your CPU/Video Card/HDD/Whatever voltages can be misleading due to many technologies of power throttling depending on usage/temperature/other factors.