Well, seven years on and my trusty T42s (see signature) are getting tired...
The 3UU started getting the old "Fan error". Actually, I knew the fan was dying before I got the first error--it was the loud 'growling' that gave it away.

That's the tropics for you (high temperature / humidity with no aircon, windows open, dust / smoke blowing all day long... ). Often I could reboot it and get it going again, but one day even that didn't work... I guess it's a good testimony for the durability of the old ThinkPads that the fan lasted as long as it did. This part of the story has a happy ending, though: I just received the long-fan I ordered (for the ATI 9600 GPU), plugged it in, and it's back in business! I like $20 fixes! Another seven years? Probably not, but I figure I'm in bonus time now, so I'm not complaining.
The 4TU might be a different story. I've got two nasty, full-height, vertical lines on the screen.

I haven't been able to try an external display, so I don't know if it's the screen (FRU P/N 92P6726; LG.Philips) or the GPU (ATI 7500). I have a dead Dell with a 14" display, but the connectors are all different... Where's standardisation when you need it?!

Anyway, if anyone has any advice on how to go about diagnosing display problems, I'd love to hear them!
The best part of this story is that my in-laws are bringing a brand new x201 over in a few weeks!

Just don't tell my T42s, or they might get REALLY grumpy.