That fault is typical of a Gen4 .. I do not yet know why but hope to get a dead Gen4 and find out shortly.
Please confirm it has A1409 on the label.. if not please give me the model number.
Anyhow.. it is dead, busted, rosak, stuffed,
With no light on.. nobody is home! !!
If you have applecare, exercise it.. Apple will replace TC up to 3years old but the rules are fairly complex..you have to have bought the TC within 2years of the computer that has applecare.. please ring and ask apple.
Other than that, you can recover your files by pulling out the hard disk.. this is not a hard disk problem.
Unlikely to be power supply either.. so I am unsure.. if you have disk still spining.