That's almost definitely just a bad power supply. We have replacements:

TiVo Power Supplies

If you want to test, the power supplies on the two models you have are interchangeable, so you could move the good one to the bad unit.

OK, I purchased the new power supply, installed it, and this Tivo is happy again, back on the network, etc.

But there's a quirk remaining. For a long while, several months or so, the colors would go funny, green would appear as blue, etc, or sometimes the color would go out entirely and I'd be left with a black & white picture. At first, I blamed my old TV especially when turning the TV off and on appeared to correct the problem, but then I realized I only had this problem with the Tivo as the DVD player never has a problem. Further, when the color problem appears, I can bring up the TV's internal menu and such, and the colors are normal for that. It's only the Tivo's output that has the color problem. Also, pressing the Tivo button and going to the main menu would sometimes correct the color problem.

When the TCD24004A died, I brought the TCD540040 down and connected it to this TV. This had an even worse problem, the colors would shimmer across the spectrum constantly and nothing I tried would correct it. Both work normally on other TVs, though. I also switched the DVD and Tivo on the TV inputs, but the color problem followed the Tivo, no matter where it was plugged in on this TV.

But when I installed the new power supply in the TCD24004A, the color problem disappeared. This makes me wonder if it's an early sign of a failing power supply? It would be a VERY early sign, though, as that problem was showing for several months.

However, after a few days on the new power supply, the original color problem has reappeared. I can correct it by switching back to the main Tivo menu once or twice, though, so it's not unbearable. So far...

BTW, before bringing up the TCD24004A on the new power supply, I plugged it into a brand new APC UPS, just as an extra bit of insurance against any irregularities in the power line, so hopefully that rules out any power line problems.

But do you have any ideas as to why the Tivo display on this TV has a color problem?

If you have color issues on two units on the same TV, then you're looking at some issue with your setup there. I'd try removing all surge protectors, UPSs, etc., just to rule them out. Then try some different cables--you might have bad cables.