TZ100/ZS100 Focus for night photography

Hi, I am desperately trying to take some good night photos but am having problems with the focus. At the moment I am trying to take shots with mountains illuminated slightly by the moon with the starts above, or a backcountry cabin with a light on with stars overhead. I can't seem to get the focus sharp in any situation. I have tried using manual focus and turning the ring all the way to the left (I have read in a number of forums that I need to focus at 'infinity') and I've also tried focusing on something as far in the distance as possible using a head torch. Neither of these have worked. The photo below is an example of what I get - everything just a bit fuzzy! 
If anyone is able to give me a step by step guide for this specific camera I would be forever grateful as I'm travelling through Northern British Columbia at the moment with a million opportunities for great shots that I'm missing!

If anyone is able to give me a step by step guide for this specific camera I would be forever grateful as I'm travelling through Northern British Columbia at the moment with a million opportunities for great shots that I'm missing!