So I understand that power surges and such can have a negative impact on PC hardware, i.e. outright kill it, and I do have a surge protector for my PC, but...
That surge protector may not be doing much for you. I used to be involved with a company that did Point of Sale installations in restaurants, and we saw how worthless most consumer-grade surge protectors actually were. At best they'd die in a sacrificial way; at worst they'd pop after passing on an unhealthy spike to everything downstream. They might be fine for transient loads in a home (ie, something else on the circuit cuts off resulting in an inevitable small spike of voltage) but they were useless in an environment where large motors (ice-makers, industrial dishwashers, etc) were cutting in an out -- and I would expect an overloaded electrical system in an aging apartment building, while not as bad, might be similar... especially when the circuit breaker is regularly reset and power returns in a surge. (Aside: no, computers shouldn't be on the same circuit as anything producing large transient loads, and in cases where there was new construction or electrical work being done, we strongly advocated creating a dedicated circuit for the PoS systems, but a lot of our customers were mom-and-pop operations and we had to deal with whatever setup they had, which usually meant the PoS was plugged in wherever it was convenient -- often right on the same socket as a fridge or something else with a motor). After seeing a lot of failures in the computer systems themselves, or the routers and related equipment hanging off "surge suppressor" power strips, we started requiring real
surge protectors -- and you could tell the real ones because they were full of copper windings and so were heavy enough to use as boat anchors or doorstops.
The good news for you is that you will get most of that for free with a decent UPS, as well as protection from sags which are probably an even bigger problem in an old apartment building.