That does not seem to be the sort of symptoms of an actual failing CPU. At most, a failing diagnostic program: I am presuming that often, you ARE noticing the effect of this CPU usage, correct? (as in, it'd manifest as some intermittent stutter and lag and the like)
If Task Manager is identifying it as System Interrupts that are eating up all that power on Core #0, then it means that there is something running in conflict there, even if we've not found it yet. It's just that it gets uglier the further it goes. For instance, it could very well be that a driver is technically up-to-date... But corrupted.
This guide here happens to repeat a bit more of the same things I'd mentioned, but does cover some more.
In short, you will have to go through every running and installed program as well as driver, and likely uninstall most/all of them before you discover the one that's causing the trouble. If you replaced your CPU, you would pretty much certainly find yourself with the exact same situation.