I called the IBM repair center again yesterday morning, got the same report that there was only one LCD known for this laptop (despite the fact that I'd quite happily used a different one for a few weeks), complained that we were going nowhere, and got forwarded to a technician, who said they'd take another look later in the day and then call me back. That never happened, so I called again this afternoon. The report this time was that they've ordered a part. Well, that sounds like progress.
Normally citi has a bunch of undergraduate interns hanging around over the summer. Which can be fun. The last few years, since Peter hasn't been teaching so much, they've been more scarce. But we had a good group of them show up at donuts this morning. They seemed likely to be smart and interesting.