09' Mazda 3 not starting.

Thank you for your response. However, it did not work. When the car first would not start the key light was blinking in the dash, so we thought it was what you said. But then we jumped the battery and it started. Now it won't start at all. When my husband jumped the battery he connected the wrong terminals by accident (1st time ever) but it still started after he corrected his mistake. Now, nothing.
I should also add that he jumped the starter yesterday and the starter worked perfectly, but the engine wouldn't turn over. Any other thoughts?

The positive battery connection on my 2010 Mazda 3 was is cause of those same issues for my car. There is a 250A fuse block attached to the battery terminal connecting ring and that ring either doesnt make complete contact with the battery so youre not getting enough volts, or the nut and bolt that attaches the fuse block to the terminal ring is not screwed on tightly enough. There is a semiconductor of somekind that bolt squeezes together. If its not a tight fit, no start but the lights work.