There's a locking mechanism on the front of the machine to prevent the removal of the hard drives. The problem is that my office seems to have lost the key with the lock in the locked position.

Call a locksmith to unlock it. It's likely that if you don't have a single key, or a tag that came with the keys, Dell can't get you a replacement key that would work. That is how it is with HP anyhow, loose a key, and the ID tag the key came with, and we can't order a spare key. We always recommend a true locksmith over do it yourself, since many of our locks go into metal and would bend the case if forced too much.