I can hear my hard drive over my 3870 fan, so not true that they all made alot of noise.
Clean out the heatsink and fan. Take the HSF off the card and take the fan off too. clean the thermal paste off the bottom of the heatsink using kitchen roll, or better yet, a lint free cloth of coffee filters. With the fan off the heatsink now, use a vacuum cleaner to get the worst of the dust out of the heatsink (don't do it with the heatsink on the card), then run it under some water. Use a hairdryer to dry it, as that will also blow off any dust rather than leave it there.
With the fan, use the vacuum cleaner on the underside, holding the fan still. You can let it spin, but it can (low chance of) damage the fan if it spins too fast.
Put it all back together and see how it goes. If it is still too loud, you are probably right that the bearings are gone. If that is the case, you have 3 options:
1. Put up with the noise
2. Take the fan off, and if there is a plastic cover over the heatsink, take that off too, and put a fan on there with cable ties or elastic bands
3. Get an after market HSF. I've got the Arctic Cooling Accelero S1 with 2 80mm fans on my 3870 and it is ~20 degrees cooler than the stock cooler was (stock was getting mid 70s, this doesn't go about 53) and was fairly cheap too. It comes with memory heatsinks and keeps them cool enough to touch (I know, bad practice, but goes to show how cool they are)