As my title indicates, my ~8 year old PC is dying on me. If I had the time and energy, I would probably fumble my way though building a new one. But since I do not, I would greatly appreciate any websites you guys could recommend to build me a custom PC.
edit: changed title
I thought this was gonna be a thread about how PC Gaming is dying...in this current age of Steam.
Might be a good idea to check out /r/buildapc. Before fielding the question there, however, I'd check out their beginners guide, and check some of the existing threads so you aren't going in blind. Offhand, I think you need to lay out your goals for the project, namely what you expect of it and what your price range is, and then figure out some placeholder parts in support of those goals.
What part is dying? My current PC at this moment is only a case from 8 years ago with literally every other component changed at least once
All the components are from when I originally purchased the PC. At the time of purchase, the components were mid-tier at best. It did let me play Doom (2016) while being well below recommended specs, but I was lucky to get an unstable 25 fps at lowest settings.
 The least of the problems is the HDD is on its last leg. Just got a warning from the PC this morning about needing to replace the HDD. If that was the only problem I'd just get a new one.
 One of the four memory stick slots is dead. Thankfully I was only using three of the slots and the stick in the dead slot functions fine in the then empty one. Probably caused by one of the two tiny scorch marks on the mobo.
 For about a week now, when starting up the PC, I get a warning that the heat-sink could not be found and the system is shutting down to protect the processor. Unplugging the heat-sink cable from the mobo and plugging it back in "fixes" the problem. And no, unplugging and re-plugging before turning the PC on does not prevent the error. I have a feeling this is caused by the PSU and/or heat-sink failing.
I am well aware that I could acquire newer, more powerful components myself and most likely assemble them safely (all for less money); however, I do not have the time nor I do wish to spend the time to looking up, comparing and assembling my PC.
Might be a good idea to check testfacts.com. There is a tech gaming section on that website that might interest you.