Just thought I'll share some info re my experience with Thinkpads T40-T42, they are basically the same and all have same problems.
First of all, GPU problem as its the main and most known problem. Bad case design is the main reason that the GPU solder balls cracks. Everytime You move your thinkpad holding two front corners, case is bending(cheap and to thin plastic without any proper metal case inside), so is the board and solder finally crack. This can be properly repaired only with a proper BGA station, dont even bother using hot guns, etc. You need to have at least preheater to heat the board from the bottom, otherwise You're making it only worse. All that videos on Youtube is only a HOW TO for a how to brake it completely.
There are two ways to fix the GPU problem, reflowing the chip and reballing the chip.
1. Reflowing is almost as good as reballing but there are two conditions. First, You need to use a proper flux under the chip to do it. Melting point, solder structure is better, etc so the flux is a MUST have thing if You're doing it. Second, You need to slightly move the chip, just to touch it and push it approx 1mm when the solder is melted. The chip will move when You push it and it will go back to its original position. All the cracks will disappear and solder structure will go back to factory structure. Leave it until its cold again and You've got almost brand new board.
2. Reballing is a proper way to do it but it takes more time and unfortunately You may brake your board by doing it. You need to take the chip off the board, solder in new balls(or buy a new chip) and put it back on the board. If its done properly with Sn/Pb balls You've got a brand new upgraded board most likely free from the GPU problem.
Few problems with it. First, there are two versions of the ATI 7500 chip, one with glue around the memory chips and the other without it. If You've got one without the glue, You need a new chip. Second thing is the glue under the chip, if You've got red dots of glue in the corners ONLY - you are lucky - your board might be still repairable. If You've got a board with a BLACK or WHITE GLUE UNDER the chip - then start looking for a new board as its almost impossible to repair it. Why? Its impossible to reflow that chip as the solder expands with temperature and move outside the chip if its glued around and it will mess up connections. Its also almost impossible to reball that chip as the contacts under the chip probably already fell off with the balls or they will if You try to remove the chip. Glue holds the chip to the board but not the balls and pads when You bend the board and they are really fragile. So...
NEVER USE GLUE UNDER THE CHIP IN THINKPADS T4X and try to avoid these boards if You're buying one.
Fan problem, its either a broken fan or a broken fan circuit. If its the fan - replace it preferably with a long one but any fan from T40, T41 or T42 will work in your thinkpad T40-T41-T42. They are exactly the same even if the part number is different. If its the board problem, then fan is controlled by U23 H8S2169(might differ with your board). FAN_FRQ goes to pin 80 U23. FAN_ON comes from pin 3 U23.
Mod Edit - Removed links to Proprietary IBM Schematics - Harryc
No audio devices - no sound.
sound card is AD1981B, amplifier is: AN12942A. Any of them could be faulty.
USB problem (I'll add later)
Processor power circuit problem. Laptop turns on for a second then goes off, and the only way to do it again is to remove battery and AC.