In many TiVo models, when a power supply goes bad, one or more capacitors show signs of failure. A failed capacitor will bulge at the top and might have discoloration there as well. If you have burst capacitors, you certainly have a bad power supply. We have a replacement TiVo power supply page. If your capacitors look fine, you could still have a bad power supply. The only way to know at that point is to swap out the part with a known good one and see if the problems are affected.
In the colored portions of the pictures below, you'll see capacitors that are bad. Look at the shape of the highlighted capacitors in comparison to the others. The colored capacitors have tops that are domed and, in the case of the last picture, have discoloration at the top.