I see the EXIF now, but have only looked at the first of the"bad pics" - taken at 1/15th and f/2. Maybe it was just down to its being too slow a shutter speed for being hand held? I have taken quite a few extremely low light shots without flash but I never go that slow, I don't think. I recently bought a soft release because I know sometimes if I don't have myself braced properly and it's a very low light situation that any shake on my part is not going to be a good thing.
What do you think?
P.S. Now I've looked at both. The first says the flash did not fire, while in the second it did. Another thing you might want to consider is upping that ISO by a lot. Auto ISO in this camera can be astounding or just pushing it up to 3200 and even, yes, 6400. It's certainly worked for a bunch of us.
I'm not exactly a technophile but I cant' help thinking that this may be what your problems were, in part - too slow, camera shake and the need for a higher ISO? I'm sure others will have more to say.