Mine is about 10 years old. The other components are less than 3 years old. I am experiencing random shutdowns, booting to a blinking cursor and desktop freezes at the end of boot up.
Since I now can't get the system booted long enough to run hardware tests on memory, etc. and since the problem has been going on for more than 3 years (I had the occasional problem before the upgrade if I left the system running for several days) and it has just started to get worse recently I suspect the power supply since that is the only part older than 3 years that can wear out. Unless the case fan can cause these types of problems. The case fan is making a lot of noise.
I'm trying to eliminate items one at a time and am starting with the power supply.
I've had PSU's last over 10 years, but shorter is possible. The symptoms you describe can't just be from a poor case fan. Replace the noisy one before it fails completely and does cause trouble But a completely failed case fan that does not cool the interior cannot cause a problem with a cold boot - there' no heat to worry about when starting cold!
One thing to check on an older machine is possible hidden poor connections due to slow oxidation of metal surfaces. With the system unplugged and you grounded, you slowly and carefully go through the entire case, unplugging every connector you can find and re-connecting it again, several times. RAM, power connections, jumpers, data cables - whatever. EXCEPT: do not play with the CPU unless you have a good reason to do it! This action often will "scrub" a little oxidation off the metal contacts to clean them. Make sure you don't dislodge one thing while working on another, and re-check all before closing up and re-powering. If anything takea s lot of force, STOP and re-examine why - you should not have to use brute force on anything.