It could be a cooling fan but it could also be be the hard drive as these can become noisy prior to failing. I would recommend making a backup immediately to protect yourself.
"degenerated into a noise like an electric razor when Windows had finished loading"
Hard drive activity reduces after Windows has finished loading so this is consistent with a failing HDD. Watch the hard drive light and see if the reduction of noise coincides with the point where the light stops flashing.
On the other hand, fan noise can reduce after the fan has been running for a period of time so it can be difficult to decide.