More troubleshooting info to add to my above posts.
Here's the simplest way to see the problem:
In Safari and Chrome (Mac), if the first thing you do after the page loads is click the 'play' button, the player seems to work ok. Subsequent clicks on another song will cause it to load and begin playback, as expected.
However, if the first thing you do after the page loads is click on a song title instead, that title loads into the 'current track' display at the top of the player, but playback does not start, and if you had to scroll down to see the player, the page jumps back up to the top.
If you then click on the play button, the selected song will play back, but with the following issues:
1. The 'elapsed time' readout remains at 0:00.
2, The 'total time' readout does not appear.
3. The playback progress bar does not appear, and clicking along the timeline does not have any effect (it should cause playback to jump to the location where you clicked)