That 3rd prong is primarily a safety ground. It literally is something that is attached to the ground down deep. There are many times on a dry winter day the past few months where if I wear my workout socks, walk across my carpet and touch my laptop it'll spark. That energy goes to the ground via that 3rd prong and nothing bad happens... hence the name.
If you didn't have it, all that energy will try to find another way through the path of least resistance. Most of the time it'll be you... if not it could fry something else.
In your office situation, I'd check your Ethernet connection. If the plug has a metal shield, that is often ground. Just hope that they did their job and is grounded all the way to the switch. Just don't have too many computers without a ground prong. Your network won't appreciate it.