Living in the dorms for a couple years meant seeing a lot of failing Xboxen, and yeah, if it gets notably louder than you feel like it should, it probably means the drive's a dyin'.
A great test of this is to just try out another Xbox. If you can't, then if game menus or game loads are absolutely ridulously slower than you feel they should be (or if audio is mis-dubbed, other loading bugs), that's probably the problem.
And actually, going off the coffee filter mention, a good way to keep the fan clean (after blowing it out with a can of air) on any of the current gen systems, is to tape a section of a bounce dryer sheet to the fan area as a filter to keep dust out.