So I attempted a factory reset and all that seems to have done is allow me to lose all my previous backups and accomplish nothing else. When I select "Ethernet" in Airport Utility it shows my TC (even though the status says Ethernet unplugged) but in my Time Machine preferences the TC doesn't show up at all.
This thing is asking to take a 24-storey swan dive off my balcony.
1st, forget about configuring the Time Machine at this point, it is worthless frustration until the network issues are 1st solved. turn Time Machine backups off.
1/ download the old version of airport utility (5.6) and try that to configure the Time Capsule
2/ keep the initial configuration very simple: open network not closed; no Time Radius etc
3/ make sure the correct settings for network password are ok in your keychain if you are unsure that they are saved
4/ turn airport off from the airport network icon in the menu bar
5/ restart your Time Capsule completely
6/ restart your mac with network turned off
7/ manually reselect your correct network
8/ open safari and verify that you got an internet connection
9/ using old airport utility (5.6) configure network the way you want
10/ configure TIme Capsule
advice: even if you are tempted, dont open newer version of Airport Utility. its seriously evil.