04 trailblazer won't start

So I haven't oh for Chevy Trailblazer the dome
lights flash real quick whenever I shut it off and it
won't start again like the battery is completely
dead. Not even a sound comes out when I turn the
key over. I jump started it and got it to go and then
it died after it rolled about 4 ft. Jump started it
again and got it to stay on, but while idling in traffic
the gauges were jumping all over the place and it
almost died again. When I got it home I let it sit
and run for about 30 minutes without the gauge
issues to charge the battery, but when I shut it off
and tried to start it again it was like the battery was
completely dead.