How does a line conditioner provide power during a brownout if it doesn't have a battery?
What a power conditioner might do is already done (and better) inside a computer power supply. Incandescent bulbs must dim to 40% intensity - and that computer must work and even start up normally. Because the power supply's many tasks include making that power perfectly normal. Anything the power conditioner, at best, might do is the same thing already inside a computers supply. Most power conditioners are nothing more than a surge protector in a fancier box.
Your question begs for a technical reply. But you must first provide technical facts. With so few actual facts, the usual myths are being posted. Especially line conditioners. Which anomaly does the line conditioner solve? All off them - because so many do not even know what anomalies cause damage. Most power conditioners are recommend only by hearsay by many who do not even know those functions are already inside the supply.
Discussing some blown parts says little useful unless you cite which ones specifically. For example, many motherboard electroylitics cannot be damaged as you have said due to circuits already inside the supply. But again, what was the electrical knowledge of the guy who installed the supply. If purchased only on dollars and watts, then many important circuits (functions) can be missing. Computer assemblers are why so many supplies are dumped into American missing essential functions. These computer assemblers do not even know what those functions are. And is why so many recommend nonsense line conditioners.
So again, which electrolytics are damaged. Those otherwise protected by the supply? Or ones located elsewhere that perform other functions?
What do most UPSes do? Connect a computer directly to AC mains when not in battery backup mode. A majority do not even know that. So where is all this cleaning and protection? Obviously, it only exists in myths.
Furthermore, when does a computer typically see 'dirtiest' electricity? When the UPS is in battery backup mode. Electricity so 'dirty' as to harm power strip protectors and small electric motors. And perfectly ideal to any computer because that is another supply function. To make 'dirty' power even from most UPSes completely irrelevant.
I can think of at least 15 things that might cause your symptoms. So many because a useful reply means you must provide better information. Notice how many know only solving one or two things will help. A majority do not even know of those other 13 possible reasons. Which says why the few who actually know this stuff cannot reply. Your replies will only be as useful as provided technical details. For example, specifically which electrolytic is damaged. Different ones fail for completely different reasons.
What more often can cause damage? Defective grounds. What bypasses so many protective supply functions? And must completely bypass all line conditioners? Safety ground. What is often defective in electrically dirty buildings? Safety ground. Nobody recommended or even discussed that 12th possible reason. But again, nobody will if you do not provide specific electrical details. All you will get is usual myths about line conditioners and UPSes by people who do not even know what these might do. Somehow they 'magically' clean electricity? Yes, doing often less than what is already inside the computer.