The problem is....I am an ex-laptop design engineer, and I just purchased a used S901 that has this same problem. Here is what I have found out:
1) Due to the syptoms seen on the display, it is obvious that there is a problem with the RAM, the RAM controller, or the solder or traces and vias between the RAM and the GPU. This would exclude a problem with the connector or bus, as a problem in that area would prevent the machine from booting at all.
2) Not having a hot-air chip removal tool in my shop, I used a small torch to remove one of the BGA RAM chips from the board, and then replace it. This improved the situation. I am waiting on a smaller torch to try the rest of the RAM chips, and the GPU. If, after removing and replacing all of the RAM chips and the GPU, the problem still exists, then there is a problem with the vias being separated, likely caused by loss of PCB lamination due to excessive GPU/RAM heat(which also likely caused the solder problem in the first place).
3) The reason that a different video card is not working in a given laptop is this: Unlike desktop video cards, laptop video cards do not have their own separate ROM containing the GPU's firmware, the card's firmware is stored in part of the system ROM, along with the system's BIOS routines. Were you to flash the system ROM with a version from a system that originally contained the replacement card in question, a different card would likely work just fine.
4) This is definitely an issue with the construction of these particular video cards, or the lack of cooling around them, and this should be covered under Toshiba's consumer protection policy, if they will admit that there is a problem.
My replacement 64Meg card will arrive tomorrow, and in preparation I have already added significantly more internal heat dissipation than was originally designed into the laptop.