There are two possibilities that come to mind. Firstly it might be a fan issue. Many computers will run all the fans at full speed for a few seconds. They do this at start up to make sure that the fans work and to dislodge any dust or dirt that may have accumulated that a low speed wouldn’t just blow out of the way. Secondly it could be something much more serious - potentially a sign of hard drive failure.
If there is something partially obstructing the fan, the blades could be hitting it and that could easily sound like a grinding noise. Fans do not necessarily spin at even rates and indeed some will run the fans for only a few seconds at full speed. The reason is to dislodge any dust or particles that have collected whilst the computer is not powered. Thereafter the fans will slow to keep on top of any dust floating around. Sometimes the blades will be hitting anything that is partially obstructing the fan. This can be mistaken for a grinding noise. This is easy to spot if you open up the computer and inspect the fan blades.
Secondly it could be the hard drive. If you suspect this - backup immediately. Sometimes, when a hard drive is failing or about to fail, it can make those kinds of grinding noises. It’s a precursor to something much, much worse. Internal destruction is usually what’s next. That grinding noise means something is loose inside the hard drive, where there simply shouldn’t be anything loose at all. That typically means that when that thing becomes completely loose, it’s going to go flying around in there and cause all sorts of destruction within the drive itself. And that kind of destruction is typically irrecoverable.
