It sounds like what you're looking for is called Network Access Control or Network Access Protection software. Especially if
802.1x auth at the switch level, as suggested by MichelZ is insufficient for your needs. (Though, I'd look at setting up a RADIUS server or w/e before shopping around for NAC solutions.)
Cisco has a version, Microsoft has a version (in Server 2008, called NAP), as do many third party vendors and computer security/AV companies. [Full disclosure, I used to work for a software development shop that makes such a product.]
Having said that, security is all about doing a cost/benefit analysis around risk. Really, the "ideal" security system is one that's more expensive to breach than what it's protecting, not an "impenetrable" system (unless you're protecting something that's "priceless," of course, then impenetrability would be the ideal).
So before buying (or even implementing a "free") security solution, you should be considering what return you'll get on your investment of time and/or money. (Or, if you're lucky, maybe that decisions' on your boss, or someone else.) Just like it doesn't make sense to buy a $10,000 safe to protect a few hundred bucks, it might not be worth your investment in time or money to establish proper NAC/NAP security, if the risk is low and/or the data you're protecting isn't particularly valuable.