The first thing one has to ponder is whether or not an upgrade or new system build is actually worth the effort. What do you need the extra power for? If there's a component, like the hard drive with Windows installed for example, that has ground to a halt and no longer performs well enough, then a replacement is likely in order.
That said, just because your PC may be running slow or is sluggish at times, it doesn't necessarily require new hardware, but could mean you need to use some tools to clear any clutter out, clean the insides of dust, or run some scans just in case you've somehow managed to pick up a virus or two while browsing online.
There's also the consideration based on who actually built the rig. Was it yourself or did you purchase the PC pre-built? Should the answer be the latter you'll likely need to open the unit up and investigate to see just how easy it's going to be to upgrade components. For systems you build yourself, this opens up new options for upgrades as you should know how everything has been put together.
Even if you opt to build a new system from scratch, it's certainly worth looking into all the parts already installed in the old PC to see what can be re-used. You wouldn't want to throw away that GTX 1080 GPU simply because you're building a new PC, right? I'd recommend leaving a full re-build as an absolute last resort. If there are various components that are old and everything is just dated, then extracting everything for the dump may be a solid option.
Taking us back to an aforementioned point, just what do you need to the PC to do? If you're wanting to crack on with some video editing but the PC struggles when it comes to actually rendering everything for output, you'll likely need to take advantage of the latest CPU, but that means you're going to likely need a new motherboard, which then could lead to new RAM being purchased.
You'll also need to make sure that anything new you add to the PC won't be hindered by under-performing components. As another example, throwing in a new CPU won't make your games run faster if your GPU is still sub-par. There's no easy answer to whether or not you should start from scratch when it comes to PC building. It all depends on what you have, what you need, and money.
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Rich Edmonds was formerly a Senior Editor of PC hardware at Windows Central, covering everything related to PC components and NAS. He's been involved in technology for more than a decade and knows a thing or two about the magic inside a PC chassis. You can follow him on Twitter at @RichEdmonds.