How do bad capacitors in a power supply cause a power fluctuation on a microwave elsewhere in the house? It doesn't. Cited are the usual suspects that have no relationship to how electricity works or the OPs symptoms.
How does replacing a PRAM eliminate an abrupt power shutoff? It doesn't. If house has a wiring defect that causes that power fluctuation, then no circuit breakers trip. Obviously. But again, it means learning how electricity works and not just blaming the usual suspects.
Most likely suspect for these symptoms is a loose wire. Often found in a junction box. Other less common problems could also cause it. But anything more is only wild speculation due to almost no information from the OP. For example, do a microwave and computer share a common neutral? One so many details necessary to say anything more. In most every case, a solution means getting an electrician to first identify and then fix the actual problem.
But again, because it was so irresponsible. That UPS recommendation is a classic most naive curing symptom. Those symptoms suggest a house wiring problem - i.e. a loose wire. Fix the problem. That UPS says how many will cure the usual suspects rather than first learn technology.
A bad computer power supply does not cause household power to fluctuate. This problem is most likely located in household wiring or the utilitys transformer.
I was going on the basis that the microwave + system shut off = once, not both instances, according to the first post. But the software commonality caught my attention (hence the mention of PRAM and permissions, as the microwave issue could have been coincedental, not another symptom of another common issue). That is, start simple, then work your way up, and both of those recommendations are quick and easy (beginning of a thorough diagnostic process that could end up requiring a licensed electrician).
Now back to the microwavce, Yes, in that one instance, it seems there was a fluctuation that affected the entire dwelling. So suspecting the power from the utility co would be the first thing that makes sense. But there's no indication of a house-wide power fluctuation the second time the system failed, though possible, and it ignores the software commonality (hasn't yet been ruled out).
So I took the approach that the house wiring may be fine (seems recent, so went with the start simple, then get more complex as things are ruled out). That doesn't mean some critical information's missing, such as the utility co. recently doing work in the area, or if there's been recent electrical work done to the dwelling. Now if the problem's been there for awhile, then a loose wire would be highly suspect. But again, I'm going by the OP's information this is all recent (both instances same day). This is why I'm thinking it's more likely the software or the utility company rather than the structural wiring in the home.
I mentioned bad caps for the system's PSU (i.e. can't store their full value at working temp), and when the load gets high enough (such as startup, resuming from sleep, when the system requests HDD use, ....), the system will lose power and go down since it can't handle the load presented to it.
As per the UPS, I agree that other possible sources need to be properly investigated first, as it could mask a serious problem (structural wiring), allowing a saftey issue to go unresolved that could cause a fire, potentially resulting in serious injury or death as well as significant property damage.