My daughter has a 2009 Pontiac Vibe, she has taken it 3 places and nobody can figure it out, it has low surging idle, power loss and trouble starting it, does anybody have a clue?

Check fuel pressure key on engine off and while starting. Also check fuel pressure while driving. Also check exhaust back pressure for clogged catalytic converter.

Thanks Brian for the advise, my husband is going to check those things today, but here is a piece of the puzzle I forgot to mention. My daughter had been in Denver for a week and the problem started when she got back, we live in Missouri. I read that they have a lower octane gas there of 85, could that of done anything?

Yes, the computer learns as you drive, and when abrupt changes happen like fuel quality and altitude, it learns to compensate, then when you get home it has to unlearn all that - it takes a while. You can wipe all the learned data and let it start over by disconnecting the battery and touching the two battery cable ends together for 15 minutes, then reconnect the battery. It’ll run like crap for a few miles but it should clear up.