PC unable to load into windows. Please help

yes on 14 year old cpu if the thermal paste has never been changed then you would want to change it. Its not crucial i only briefly mentioned it because the real thing is that you want to replug the CPU as a test but when you are there you might as well change the paste.

Computers work until they don't those CPU are cheap as chip you can always just get one from ebay and replace it.

The fan jolting like that usually means the computer is stuck so the CPU is not doing what it needs to do and the bios is not coming on. The jolting is because the CPU is resetting itself to try again. Generalization here but its along these lines.

Hard to say it can last a long time really like 14 years is not unheard of i have seen computers from the era and earlier with the original paste and they work no problem, but the temps will generally be right at the end of the scale.

The CPU would be the most logical because its presenting those signs but computers are minute it could be anything on a computer this old.
The motherboards can be expensive depending on locale because they are semi collectable now and this generation was a strong one the fires i core series in existence so they are collectable in that regard etc.

in my country they go for prices close to modern ones in some cases. The one you have is low mid tier so it should not be that expensive.
There is a whole lot of replacement ones though because they made lots of variations with these motherboards so the selection is big.

These are a strong platform though so it would take a lot for them to die especially if you run them stock and they have good caps on them, The platform overall is good because they entry level boards are just as good as the top tier ones in terms of robustness. They just have less features.

i would try to re plug the cpu first if that does not work then replace it again they are cheap you can get them from china for like 10 bucks or less

You can try taking out the RAM and placing back them in correctly. I know you haven't messed with them, but it possible one got slightly loose somehow. Happened to me once.

No because the issue is before the hard drive is even loaded