Advice needed

I think you'll find all your answers in one of our other forums (this one tends to be where all the riff-raff congregate - albeit knowledgeable, well-meaning, but silly riff-raff).
 
There are three forums that should check out here: 
 
Computers
Hardware
and...
Software
 
I'm guessing all you need is in the first one (Computers).

I'd check the fans and filters for proper operation and air flow, just in case your computer inhaled a cat's worth of fur over the years.  That literally DID happen to my son's laptop - it would run for about 10 minutes and then just die.  Opening it up, I discovered that the two intakes for the fans were clogged by fur from all 4 cats.
 
Even if no clogs, fan bearings can wear out and the spin rate would drop drastically to eventually just quit working.
 
 
Bob Bone
 

If a replacement PC is needed, then I'd suggest a laptop only if you need mobility.

Desktops almost always have more of everything, be that cpu, disk or RAM, per buck than laptops. HDDs also tend to be the 5400rpm variety.

When you buy a laptop you are also buying a screen, which is often the most expensive component in a cheaper laptop, a battery and a keyboard/touchpad. And laptops are (mostly) designed with a view to keeping power usage down to improve battery life so use lower power drain components, which means cpus in particular are usually not as fast as the ones in a similarly priced tower/desktop.

Laptops also have the disadvantage of often needing even more bloatware removing than desktops, possible issues obtaining proprietary drivers from the manufacturer in years to come and can have "tuning" difficulties for DAW use, especially if the full BIOS settings aren't accessible.

If you think something in your PC might be overheating it's worthwhile downloading one of the many free temperature monitoring applications to see what the various temperature sensors are reporting. Sometimes the BIOS screen lets you see at least cpu temperature, though that needs a reboot and entering the BIOS, and the cpu etc. will cool off a bit during the reboot.

Modern Intel cpus shouldn't be overheating to the point of failure anyway, they're designed to throttle their speed if temperatures get too high to the point they can almost shut down to protect themselves. Though one that's gone faulty might not be doing that of course.

The symptoms being reported could be down to the cpu, motherboard, psu, RAM, drive controller, graphics processor.... One of those things that's horribly difficult to diagnose. Personally I'd suspect the gpu or faulty RAM as the first place to start looking but that's only a guess...

It might be worth looking to see what the system logs say in case there's something relevant in there.