Inspiron 3847, fans won't stop revving, #2

Greetings, fellow users, and Happy (post) Thanksgiving!

          The CPU fan in my machine has been "revving" for some time now and despite the supportive advice that I have received thus far from this community, the problem has not been resolved.  The other day it sounded as if an airplane propeller was about to take off--and then it suddenly stopped.  When I restarted my computer some hours later, I got a black screen (not exactly the BSOD, but close) that said: "CPU fan failure: press F-1 to continue". The fan still "revs" but now I am wondering if the fan's motor is beginning to literally burn out. The black screen also offered another way for me, and that is to press F-8, but that will take me into the BIOS, and this is an area in which I am not that well conversed. (My personal maxim: If you don't know what you are doing, then don't do anything.)  So, I need help. There is no way that I can procure a new replacement fan for a computer I purchased eight years ago (the pc itself is no doubt older), so I am left to consider "used" fans (on eBay).  I don't know if I should trust any item that is listed as "used" but at this point, almost anything will do to keep the machine going.

     The computer begins to overheat at the outset, and I have to turn it off and on again for it to temporarily stop.  I thought that it might be the CPU itself and bought a new one (with the same specs) but that didn't solve the problem, either.  I ran a diagnostic test on the CPU fan and this is what I got:

Error Code:  2000-0511

Validation:  107 804

     If there is anyone out there who can understand this message, I would appreciate it if you could let me in on it. 

--Cartoon Man