Check hardware first then software. Air in a can is a joke.
I don't work in IT but CAD support. Funnily enough users came to me with their Slow woes, instead of asking IT techs and being fobbed off with nonsense jargon.
Most IT support don't know anything more than they have been shown. Hardly any ever check the event logs or know how to trouble shoot properly.
It's more uninstall, reinstall and hope it works.
One of the first things I used to do to a new built CAD PC was defrag it as they always had 25%+ deframentation.
The IT Crowd is so funny as it's based on reality. BD
In corporate domains old hardware usually doesn't survive.
Sometimes its given to users and just written off.
I've fixed tons of desktops and laptops and it is usually an issue of cleaning, reseating and using cable ties to replace broken fan assemblies.
'Bugs in the machine' is common problem too.
IT departments don't bother much with hardware, but a laptop often slows down just due to fluff.
IT give it a shot of compressed air and then declare it dead.
I remove the keyboard etc gain access to the fan assembly and open it up. Never fail to find compacted fluff which the fan still spins in. From ouside the fan looks clean and spins
(often a bit slower than usual)
There is no longer enough air flow over the MB.
Good sign for this is a high HDD temp and/or CPU temp.
Old thermal paste gets eaten by bacteria that make bubbles so heat doesn't conduct.
Lot's of laptops with Nvidia and ATI just stop working as the solder on the GPU mirco fractures.
The tip about using laptop desks is good but also check the rubber feet are all there. if one corner is missing even a flat surface with block air. I fix missing feet with extra thick sticky back cloth pads or rubber feet taken from other broken PCs. Dab of super glue and good as new.
Not every one can afford a new PC every 3 yrs.
An 8 yr old PC can easily do what most people want it for.
Installing Linux for research/learning is ok, but for most people I still think it best and easiest to stick with the original OS/Apps.
Of course if the Raspberry Pi can be manufactured on a big enough scale.. I think there will be a lot of old PCs being scrapped so if you want to upgrade memory or HDD check out local FreeCycle sites or buy a Raspberry if you can.
One of the worst cases of PC abuse I ever saw was at an Oil Refinery.
Had to ride my bike out to the place and was supposed to fix/replace the graphics board.
It was placed on a table by an open widow in a prefab hut.
Opened the grubby filthy unit and just laughed.
It had probably gotten very dusty but was now completely covered in oil. I just plled out the plug coiled the wire up and threw it in the bin. Then told them it was NOT to be used and skipped.
2.5hrs travel there 2.5 hrs back for 10 mins support.