is it true that a computer will slow down after it is used for a long time?
Well let's just ignore the software bloat aspect of computer slow down and look at things on a piece by piece basis.

CPU, MoBo, Memory like caches and DRAM:


NO, these are clocked systems and the clock is designed to drive the system just fast enough to make sure that the device finishes one task before starting the next (in simplistic terms).  These clocks do drift and age a little, but that is measured in PPM (parts per million) if the part slows down enough that it can't keep up to the clock, then it starts to have major problems.  Like most things digital, it runs until it , .... well doesn't.


That really just leaves the HDD:


It is POSSIBLE that this will slow your machine down.  We  do know that there can be corruption in the stored bits (bit rot) and the operating system can mostly correct these.  But in reality these tend to cascade and then go south very quickly or else they happen at a consistent background rate (which wouldn't affect this premise).
I would say that there would be some machines that slow down rapidly and spiral out.  Otherwise the effect will probably not be noticeable.


On the whole, I'd say nonsense.