Whenever I would follow a band's link to their page at ReverbNation and I'd click on one of their songs, the PLAY icon would blink a few times but nothing else would happen. So I did some research and found a post by "Scandalous Lovers" here that revealed the answer.
Basically, all you need to do is wave the mouse over where the music player should be for a few seconds and it will come to life.
Here are some pics to prove it.
When I first bring up a page at ReverbNation, it looks like this:
The flash player is supposed to be in the upper right corner, under your username, above the "chart position". So, wave the mouse around that area for a few seconds and the player should appear, like this...
Once you move the mouse away again, the player will reduce to its normal size, like this...
I read somewhere in the thread that I mentioned earlier that you might have to increase the local storage space to get some songs to play. Once you have the player activated, that's easy to do. Just right click over the player and select "Settings..."
Then on the next pop-up screen, select the 3rd tab from the left (with the folder icon) and increase the storage from 100mb (the default) to something bigger (eg, unlimited).
Hopefully, that will help some people get ReverbNation to work.
Just FYI, I am using the Firefox browser on a 64-bit Windows laptop.