I may have found a solution to this issue. First, let me note a couple of things so anyone reading this can determine if it may help them. I have an older 15 inch MacBook Pro (about 5-6 years old) and an LED Cinema Display (27inch). I have it running the most up to date OS and all SW is updated. In fact, when I tried to update the LED SW and firmware, the system indicated that I don't it. Anyway, the monitor belonged to my wife, who was using it with no issues on her 6-7 year old 13 inch MacBook, and no longer needed it as I got her a new iMac with a big monitor. So, I inherited it. But when I plugged it in, just got black screen. There was definitely a connection as the screen on the MacBook Pro seemed to dim out and then come back. After reading about, in this thread, people jiggling the connector at the port, I had an idea (as the jiggling didn't work for me). I eased the connector out about an eighth of an inch, to where it was at the point where it was causing the laptop monitor to dim and lo and behold, the LED Cinema monitor comes to life. I've tried this several times. If I push the connector all the way in, black screen. As I ease it out, to just the right amount, it pops on, and stays on. After choosing the USB out put, from the sound preferences, the speakers in the monitor work too.
Now, I will say one thing. It is a little sensitive to lateral motion pulls on the cable at the computer port, so make sure there is no tension on the cable. With the cable partially pulled out, to make this connection work, it must experience more torque, due to any pulling on the cable, and that can cause a break in the connection.
I know this is not intuitively sound, but it worked. It's like plugging into a wall socket part way. It was as if the connector from the monitor (the metal parts that go into the port) are too long by 1/8 inch (give or take a 1/32) and you have to account to that by pulling it part way out. Anyway, try this as what's the worst that can happen? You may find the monitor is fine, which is why it worked at the store for some people who wrote in this thread, and you don't need a new one. Hope this helped.