Hmmm, thanks for the suggestion. With a drive jumpered to slave, and a cable borrowed from my PC, I now have the "option" of having it hang at the welcome screen, rather than cycling from there. It's different, but I'm not sure if it's helpful. When jumpered to master, it behaves the same as with the stock cable and cable select jumper. I think I can guess how "cable select" works now.
On the old 40 conductor cables, where all 3 plugs were electrically and physically identical, pin 28 was connected at the motherboard end and at the middle connector, where the master drive was connected, and, if jumpered for cable select, the master detected that completed circuit (to ground) on pin 28, and declared itself as master.
On the far side of the middle connector a hole was punched through the wire in the pin 28 position so that the drive at the far end of the cable couldn't detect anything on that pin, and, if jumpered cable select, it detects that it's not detecting, and declares itself the slave.
The problem with this is that if only a master was installed there was an unterminated stub of cable, which reflects signal back from its empty end, which served as a form of interference.
If your 40 conductor cable didn't have that hole punched in it you had to jumper the drives differently to make one declare itself master and the other declare itself slave, but you could put either on either connector, or even plug the middle connector into the motherboard and put the drives on the two ends. If you only had one drive you put it on the end and left the middle unconnected, which properly terminated the cable.
The newer, more aggravating, 80 conductor cables feature 40 pin connectors, but each of the three has a unique internal wiring scheme.
The plug on the far end (the black one) is intended to always be the master and the one in the middle (the grayish or beige-ish one) to always be the slave, and the one on the other end farthest from the middle one is always the motherboard connector. The motherboard connector is blue, or, in some cases, green.
Pin 34 in the motherboard connector is internally connected to ground, which signals the motherboard that an 80 conductor cable is in use. The corresponding wire does not connect to that pin in the motherboard connector.
That wire is connected to pin 34 of the slave and master plugs, and the 2 drives talk to each other over it.
The motherboard and master plugs (on each end of the cable) have pin 28 (cable select) connected to the corresponding wire, so that the master detects that the motherboard socket has that pin grounded and knows that it's the master.
The middle plug does not connect pin 28 to the corresponding wire, so the slave drive connected to it doesn't detect a ground on that pin and knows that it's the slave.
Sometimes you can use an 80 conductor cable with one drive jumpered as master (instead of cable select) and connected to the black plug, and the other drive jumpered (or un-jumpered in some cases) as slave and connected to the middle grey plug, and get away with it, and sometimes it just confuses the computer and/or the drives. Depends on the particular hardware involved.
As someone once said "Standards are wonderful things, that's why there're so many of them."
As best I can tell, the welcome screen is on the TiVo motherboard, and the "just a few more minutes" screen is on the drive from which it tries to boot, so if you get the second screen it's having at least limited success in reading the drive.
It would be useful if you could telnet in to the boot process and see what the TiVo has to say.
Don't give up until you've tried with an older 40 conductor cable as well as an 80. You might have a 40 hanging off of your CD drive.