First, it crashed several times over a month and had to be power cycled.
Then, it wouldn't turn on at all and just made a tick, tick, tick, tick noise.
This is what I did to fix it.
Step 1: Change Bad Capacitor
The original was a Teapo SC series, 2200uF 16V, low ESR capacitor. I replaced it with a Nichicon PW series, 2200uF 16V, low impedance capacitor, part number 647-UPW1C222MHD from Mouser Electronics (who have no minimum order).
Just for good measure (and because I bought more than one) I also put a capacitor in C31 which was not stuffed in the original board.
Be sure to use a low ESR (also known as a low impedance) capacitor.
If you don't, it may work in the beginning but will quickly fail.
All electrolytic capacitors have a limited operating life (measured in thousands of hours), so this is an especially weak point for devices that are always powered on.
Be certain that the white ribbon cable between the power supply and the main board is plugged in all the way. It can be misaligned and short contacts causing irreparable damage to the power supply and the main board.
I have only done this with a Hughes HDVR2, but weaknees.com says the same power supply is used in the Hughes SD-DVR40, SD-DVR80, SD-DVR120, the Philips DSR7000, DSR704, DSR708, the RCA DVR39, DVR40, DVR80, DVR120, and the Samsung S4040R, S4080R, S4120R.
WARNING! The power supply includes unshielded contacts that are directly connected to line voltage. THIS CAN KILL YOU. Do not work on a power supply when it is plugged in. Do not work on power supplies if you don't know what you are doing.
I did not say how to desolder and replace the capacitor. If you don't already know how to do this, you should not be working on power supplies.
This is only a report of what I did to fix a Tivo. It is for educational use only.