Is there a "trick" to shooting in low light without a flash?

Today is the first time I actually had a chance to use my new J1 with kit lens in a real world situation. We went to a restaurant that was surrounded with windows and had overhead lighting as well. With my own eyes it did not appear to be dim whatsoever. However, my J1 was absolutely blown away by the lighting conditions. I had to set the exposure at its highest setting (3.0) just to get a somewhat bright picture. I have my ISO set to auto 100-3200 and even at 3200 ISO the pictures were still dim. I am really bummed out since this camera will be used 80% of the time indoors at parties and such.

My next question is would investing in a better lens such as the 18mm f.18 make any noticeable difference? What about filters? I have about 20 days left to get a full refund on my camera and am at a loss as to what I should do? I am trying to avoid using the flash because the photos look washed out from its powerful led. I really feel like my crappy Sony TX-7 could have taken better shots than these. Either that, or I just suck at taking pictures.

I really want to avoid having to use Lightroom or some other program to "fix" what should not have to be fixed in the first place.

Super dark, even though there is windows behind me and to the left of me.

Same situation here..it's in the middle of the afternoon with the sun shining and it came out like this!

This is the best shot I took. Light coming from behind them and all the windows to the left as well.