If your TiVo is on the initial boot screen then it is not reading the hard disk. That screen is embedded in the mainboard PROM. Try it: remove the hard disk and power on again and observe what happens. The TiVo should attempt to reboot after about every 30 seconds and return to this screen. Given you have two others (as per your signature), why don't you first try and exchange a hard disk temporarily to test this?
The "tick tick tick" power supply is normal if you have disconnected it from the mainboard and hard disk. It needs a load to function. You can simply plug the hard disk only back in and verify it starts, and then verify you have roughly +5VDC from the red wires and +12VDC from the yellow wires with respect to the black wires. Given you still had the "welcome" screen I do not think power supply is your problem here. Although your comments about failed capacitors is valid, that is extremely rare with the S3 power supplies.