sorry for replying late...
You wrote "my coworker is a Quark guy and dooesn't use my files over the network" , this means your file are on the network and this would be the same place your IDLK file would be.
Hence could be permission issue which could be modified by network admin not sure right now, but to test you can move one of the file on the desktop and then check , does the idlk file gets deleted when indesign is closed properly or not.
Our computers are networked, but we don't use a central server. I tried your suggestion and it worked, but what I don't understand is that we've had this same configuration for the 5 years I've worked here and this just started happening. If it was only on my CS5, then I woul just think is was a CS5 or Snow Leopard issue. But since it is suddenly doing it on my old computer running the CS4 version and a different OS, it doesn't make sense.
@jensapp--as I have said it may not the issue with your computer or application but could be because of the changes made at the back end by your network admin on the permissions, hence its worth checking with him/her .
@GeofferyH--Its not mandate to be the netwrok problem , as I said it is more of the permissions problem , check the location where these IDLK file are , try changing the location to desktop or somewhere else and then open the Indd file and check.