Mass Effect 1. Finding Liara T'soni on Artemis Tau. Can't input code into mining laser to free Liara or escape location

The code is randomized.  You need to use trial and error, memorizing the inputs that will clear a ring, and avoiding the ones that send you back to the start.

I believe the code is random. The one I input was up, down, up, down, down and it worked. The minigame doesn't kick you out if you miss one, so just remember what  the progression is and it will eventually work for you. Just remember what directions make the center circle go green.