Welcome to the Thinkpad Forums
Well, the easiest things to look for first are external; cracks, LCD response, keyboard functionality etc. Make sure that the hinges fell tight enough for you and that the screen isn't warped or the Chassis/LCD otherwise cracked, bent, or yellowing. Next, take a look through the BIOS and make sure that all of the settings are at default and there are no Power-on Passwords, Supervisor Passwords, HDD passwords, or any other custom user entry set that you don't know about. After that, check to make sure that it can boot through the BIOS splash screen and load an OS correctly, listen to the HDD and, if possible, check its SMART attributes with HDTune; you can use a portable USB stick and put the utility software on that, speaking of USB, check to make sure that you can transfer across USB at the right speeds...HDTune can bench that too. Check to make sure the optical drive, the network cards, and all the ports on the outside that you plan to use work as well. It would also be good to see if the T42p can suspend/hibernate/resume properly, using a minimum of tasks in windows, as well.
Finally, for the planar/mobo problem, *gently* flex the lower right hand corner and the upper left hand corner during several boot ups; if it hangs or the graphics get distorted, then there is most likely a hardware problem.
That's all I can think of for now, I will post back if I think of any more. HTH
