I had a similar problem on 3 different computers. My desktop was constantly crashing with a blue screen with the message (CPU fan has failed). At other times it gave me a message about Clock interrupt on CPU core 2 & numerous other different messages with every shutdown when it bluescreened.
I called HP Tech support & fooled around with this problem - I tried replacing the hard drive because kept getting shutdowns with messages like hard drive corrupted, file errors and so on. I tried PC Doctor but never could isolate a problem. This went on for 4yrs.
I was reading a blog on HP TECH. problem/solutions & saw a mention of CPU/Thermal Paste/Overheating. I checked the heat sink on CPU & the Thermal Paste was hardened, heat sink was clogged with dust & the fan that sits on it & pulls air onto it was full of dust(like a vacuum cleaner).
I ordered Thermal Paste from vendor on EBAY & I cleaned the CPU & heat sink surfaces with brake cleaner or alternately use 70% or 91% Alcohol. Then I applied small amount of Thermal Paste & rubbed it back & forth till it was evenly & thinly applied between Heat sink & CPU
I've fixed multiple systems of different ages that "Would not boot" by taking it it apart, removing the heat sink & fan, & cleaned thoroughly,removing the old thermal paste to apply new thermal paste to CPU/HEAT Sink Surfaces. It booted right up & everything started working like it was new.
I can tell you right now that compressed air will only make it worse, since it just pushes the built up dust deeper into your computer housing and does nothing to actually remove it.
If you remove the heat sink or any component that has thermal paste, you must clean and reapply thermal paste. I've found that with systems more than 5 years old, dust built up causes systems to overheat and run hotter.