Is the back of your rack open or closed? I have a rack that came with a back door, but my equipment is too deep, so I just took it off. So all the hot air from my equipment blows out the back and doesn't get trapped inside the rack enclosure. So while there are cutouts for rack fans if I wanted to use them, I don't see the point. In other words, if the back of your rack is open, I doubt you even need those rack fans. And if the back of your rack isn't open, open it up and disable those top fans.
Can we get the specs on your hard drive stack and server?
Also, are you running any thermal monitoring on your hardware? Generally, cooler is better, but if you're using all those fans to keep the hardware at ambient (room) temperature, that's overkill.
Another approach is to figure out what is making the most noise in your server rack. It's the same concept we use in individual PCs: usually, there is one component that is the loudest or most obnoxious. What you do is go through each noise-making device (usually fans) and disable them one at a time. You might want to start with groups of noise-makers in the interest of time. For example, turn of all those top rack-fans---how much is noise reduced? Turn of the hard drive stack---does it make a noticeable difference? Turn off the server---how's it sound?
The idea is to find the "low hanging fruit", and work on quieting the loudest devices first.
Another take on those top four fans: if you have the equipment, cut a giant hole in the top of the rack and replace the four fans with one much bigger fan. The idea being that you can get a bigger fan that runs slower, and is thus quieter (without sacrificing airflow).
You said you're on a tight budget, so spending big bucks probably won't be your thing, but... I recently found I needed a bigger switch, so I ordered the HP J9078A 1400-24G
. It's rackmountable and fanless. (I'm currently using its little brother, the 8-port version of the same line.)
If you decide to upgrade your equipment, take a look at my rackmount file server
. It's not silent, at least by SPCR standards, but for a system with eight drives, it's pretty quiet. I monitor temperatures very closely, and I'm not concerned about any heat-related reliability issues.
I also like the ideas others have mentioned that involve building a three-sided enclosure for the rack. You could build and intake vent at the bottom front of your self-made enclosure, and even get fancy and have some ducting vent the hot air up to the ceiling or even into another room. If you can vent into another room, then you can have attach a high-power "suck" fan to the duct, and really move a lot of air through the enclosure, without too much noise (in your office anyway).
Good luck. Keep us posted on your progress!