Usual suspects are
1) dust or something (say a wire from something else) in the path of the blades. Blow it out/move it out.
2) The blade section stuffed on the motor have come loose (either going at an angle or rising up/lowering down) and is hitting against something. See if you can sort it -- most computer fans are just pressed onto a spinning shaft rather than keyed or pinned to a flat or something which makes life easier, though some will also bend things out the way or file down a bit of the fan blade assembly (minor differences in shape can make major differences in efficiency, noise or whatever, and we can have a nice month long lecture series on fluid dynamics for fans if you want, but at the same time meh for a fan like this if you are only taking something off with a needle file).
3) A bearing somewhere in the mix is broken. Can mean replacement (which probably means replacement fan assembly, or rigging up some kind of replacement setup from something you might be more easily able to buy) or tearing it down far enough (might be a simple seal, might be something more*) that you can get a drop of oil in there -- try to know what you are doing there as squirting oil around the place is usually less than ideal.
1) is most common and easiest to fix. The others are failures at some level and can be harder to sort, you can however usually tell what goes and possible indicate to yourself if you apply a bit of pressure during operation (pokey stick, screwdriver, finger... I have used all of them). After things "get to temperature" as it were in the assembly then it might stop, or might even get worse.
Resonance I would usually expect to be there from the start but a motor on the way out and some dust might change the harmonics such that it hits it. Not to mention you say this happens at any speed.
*this is for a desk fan but I have seen similar setups inside computers on a smaller scale.