Not too long ago, I found a used gigabyte windforce gtx 770 for sale. I i bought it and installed it into my gaming rig. As i turn it on, it boots fine but the middle fan is making a rattling noise, it is not coming in contact with the frame though and when the fan speed is below 50 in msi afterburner, it stops rattling.
Seems like the fan might need replacing or there might be dirt or debris inside of the impeller's motor housing. Got a model for the GPU? An SKU should help narrow down the card...and you should be able to find replacement fans on Ebay.