Quiet grinding sounds when I turn my computer on

[Acrylik]

For about 2-3 minutes when I turn my computer on, there is a very quiet, grinding kind of noise. It goes away, and I don't think my computer is running any worse since it started.
I just want to know, could this be something that will end up bad?

 

[batuchka]

A simple check is open up the case and check if any stray wire/s are touching the case/cpu fans just a wee bit?