Time Capsule will not turn on
Spontaneous turned off and will not turn on again.
Time Capsule 802.11n (1st Gen), OS X Mountain Lion (10.8.2)
It is a gen1.. 4years or more old.. it has reached End Of Life.. EOL.. RIP.
Time to buy a newie.
Or do some fun DIY repairs.
Most Gen1 died long ago.. yours is the last survivor of an ancient race.