I have a 2006 Trailblazer anda week or so ago I came very close to running out of gas... I made it to the gas station just in time. But since then I sometimes, but not always, have had a little trouble starting it... like it's not getting enough gas. Then last night it started, but then just as I was pulling out of my driveway.. it died. I had no trouble restarting it, but when I got home I turned it off and tried to restart it... it hesitated and wouldn't turn over.. I tried a few more times with no luck... then when I turned the key... absolutely NOTHING would happen...dead silence..the panel lights came on and that was it.... the motor would not try to turn over at all...the battery would not even clickIt was like the whole ignition system just shut down... and I can't even get it out of"park".

On the fuel issue, there may have been some trash in the tank that got sucked into the pump when the fuel level was low. First thing to check is the fuel filter to see if it's stopped up. If it's not that, then the fuel pump may have sucked air and been damaged.

On the no starer issue, have you tried checking your battery terminals? If the terminals get loose or corroded, they can act like what you are describing when there's not a perfect connection.

Good luck.