This can happen through a hardware defect of the touchpad. It did, in my case.
That's right: a defective touchpad, even though working flawlessly as a pointing device, can prohibit the proper recognition of the trackpoint. This seems to be possible because both are supposed to act as PS/2 active multiplexing devices – needed, because "normal" PS/2 only allows one keyboard and one mouse. And that's how they could interfere.
To see if this is the problem, either disable the touchpad device in BIOS, or physically disconnect it. (Be sure to switch off the computer and remove AC plug and battery before you disconnect it!) If the trackpoint starts working now, your touchpad seems flawed and should be replaced. The touchpads of ThinkPad T61 models are compatible. Independent of screen size, though that affects the touchpad cable length and is not an ideal fit (the cable can be exchanged individually, though).
Under Linux, the probing for PS/2 pointing devices happens in the i8042 PS/2 chip's driver. There are some options that might help you to fix the probing without replacing the touchpad, or at least to debug the problem. I did not have luck with that.