speedtest.net is also accurate, and you have the option choose several servers for testing the download and upload speed.
additionally there is a qute utility called pingtest, which allows you to test packet loss, ping and jitter.
In wireless networks, with the help of pingtest you can accurately identify the maximum optimal distance from the router/repeater. (the further you go from your access point, the greater the packet loss)
You didn't mention if the company is wired to the network or wireless.
If is wireless they may not have a uniform coverage for all their computers.
For that you can also use NetStumbler
If they have wireless access points and security is not good enough or poorly implemented, they may have "kneibours warriors" doing the piggy-back on their internet connection, etc etc.
If you take your time to put a proper plan of action in place, it is impossible not to find enough bottlenecks to improve the speed.
Get someone with you, I don't know AngryGeek, but if he can drive by for one day, and if he agrees you may benefit a lot from having someone with you, even for just one day.
Edit:
Make the P2P problem a priority. On a 10 mbps dsl connection over telephone wires for example, is enough to have two employees downloading torrents and you'll feel the speed difference.
