Time Capsule connected to internet, however does not show up in network.

Is the TC plugged into the computer by ethernet? If not do so.. it doesn't matter if the TC is out of the network.

Press and hold the reset again and set the TC to the correct mode, ie router with bridge or pure modem.. bridge with the modem-router. Set the wireless to a new name.. short, no spaces, pure alphanumeric and give it another try in the network.