I installed Lubuntu 12.04 on an old Thinkpad T20 I had lying around. This machine is giving me a few headaches. When I shut it down, it freezes and I have to switch it off manually with the power button.

I wonder if this helps: when it freezes, it shows the Lubuntu shutdown screen with the dots below the name. Three dots are blue and two are white. Maybe it can be a rough indicator for where it freezes?

I know this is difficult to diagnose remotely and that more information is necessary, so I'll put up any additional stuff that might be useful (logs and so on) that you guys might suggest.

Well, that's interesting. I tried to leave the laptop alone after it froze, and after around 30 minutes, maybe more, it went in sleep mode. Not a screensaver or a blank screen, but actual sleep mode (or hibernation? Not sure). When I pressed the power button again, I got back to the Lubuntu shutdown screen with three blue dots and two white ones. I'm going to leave it alone again and see what happens.

Forgot to update this thread, for all there is to say. After leaving it alone, it would just go to sleep again, with no real progress towards shutting down.

I tried a sudo shutdown -h now and it has the same problem.

Ideas?

Interesting. I have a few questions. Before you installed Lubuntu 12.04 did you check the MD5sum on the download? Did you get a good burn on the ISO? Did everything work after you installed it? I am assuming that you have enough RAM to Hybernate. Is that correct? I am also assuming that this is the only OS on the computer. Is that correct?
If there isn't a great deal of data on your machine, the easiest thing to do might be back up your data and reinstall.

I have the same problem with a Thinkpad 600X. With 327MB of RAM memory available, I have successfully installed and run Ubuntu 11.10, Kubuntu 11.10, and Lubuntu 12.04, and they all seem to boot up and run fine (except for not properly configuring the Xircom PCMCIA network adapter yet - something for a different thread..). But in all cases, when I shutdown, it goes through the shutdown sequence up to a point and then stops with the shutdown screen with the three dots. Every time I start it up after that, it acts normal except for those two problems: no network and incomplete shutdown.

Can you post the output of sudo shutdown -h now, or at least the part where it hangs and does not shut down.
This may provide some clues as to where the problem is.