I have found a solution and am posting my write-up for everyone.
Luckily, this is not caused by file corruption. Based on what I have been reading in this forum, it is presumably caused by a damaged playlist entry, probably upon import of the song into Itunes from another location, such as a backup.
The bad entries can be reliably and easily found by playing each song in your library and jumping to the end. What I discovered by analyzing where the songs broke is that, consistently, only 4 minutes and 10 seconds of any broken song would play. Why this is I don't know, but it shows that Itunes is breaking the entries in a consistent manner. It's also helpful to know the cutoff point of your broken songs, since, once you've established it by finding a few of them, you can fine tune your identification of songs that break off very close to the end by sorting your library by Time. Hover your mouse cursor very close to the end of the playbar and allow each song to play to the end; if the song is not broken, it should count down all the way to :00. Then, once Itunes advances to the next song, just click on the mouse to advance that song to the very end, and so forth. If you hover your cursor near, say, the :03-second mark of the playbar, you should be able to go through about 20 songs per minute. In my case I was able to find a few more songs that were just a few seconds longer than 4:10 and which broke off very close to the end.
In my case, whether Itunes could have broken any song shorter than 4:10 I do not know. Out of a library of 225 songs, I didn't find any. Only eight of my songs were broken, they were all over 4:10 in length, and they were all imported on the same date.
If the entry is bad, the song will refuse to play when you advance the playbar past the cutoff point. Itunes will simply move on to the next song.
Also, going on the assumption that these entries are damaged in a batch import, you might be able to quickly isolate most or all of the other damaged entries by sorting your list of songs by the "Date Added" field, and then performing the steps above to confirm which entries are damaged.
Once you have your list of damaged entries, the solution is to delete the song from Itunes and then re-import it. First, however, right click the song and choose "Get Info" to identify the file's location on your hard drive. Then, right-click the song and choose "Delete." Itunes will ask you if you want to move the song to the Recycle Bin. This is not necessary and will only force you to restore the song from the Recycle Bin, so just say no by choosing "Keep File." Then, you can import the song back into Itunes in one of two ways. Both methods work, but I find the first method to be faster. From within Itunes, click on File | Add File to Library, then locate the file on the disk and import it manually. Outside of Itunes, you can locate the file on the computer and tell it to open in Itunes, and it will be imported to the Itunes library automatically.
-Paul Ronco, Computer Technician