The oldest "part" I'm currently using, is an entire eMachines T-5026, which will turn 13, next Valentine's Day. Still going "strong" (*), I might add!
Other than a new DVD drive, and some constantly migrating HDDs, the "newest part" on the machine, is an Antec EA-380 "Earthwatts" PSU (**), which in itself is in excess of ten years old. Noteworthy is the fact that the OEM HDD is still in it, as the "C/:" drive. It's a WD "Blue" 160GB SATA I (!) (I think WD called their "Blue" models "Caviar" way back then).
As far as my newest project goes, (i5-6600K- X170), The oldest part is the case I took from another rig, an original CM "Storm Scout" model, and the copy of Windows 7 Pro 64bit SP1, I had laying around for a few years as well.
(*) "Strong", is a relative term when discussing an Intel P-4 519 single core "Prescott").
(**) The Antec EA-380 was a warranty replacement for an earlier 350 model which was discontinued. As expected, the original eMachines Bestec failed within a few months, as did, surprise, surprise, the Antec I replaced it with. The Bestec was a 300 watt model, which was courteous enough to simply die, without taking the motherboard out with it. (y)
Now I have a question. Since my eMachines is at or near the age of puberty, will it start to grow hair or fur like the computer in the article?