The only devices right now that are a part of the network are the there you said I should reset: the modem, the Time Capsule, and the desktop. Unfortunately, I don't have any other devices with which to test that particular hypothesis you have just mentioned.
I did go into the Advanced section of Network Preferemces though, and noted two things:first, it says that it has a self-assigned IP, and second, there is nothing listed under the DNS tab.
I'm assuming that second observation is an indication that you are correct in saying that the computer has no DNS information. If that's the case, how do I go about finding that info and what do I do with it once I have it?