Welcome to the forums Dottie!
If all was well before the battery went dead and now it's doing this, it's probably still a REALLY DEAD battery.
Charge it overnight, swap it out with a different vehicles battery, OR try using jumper cables. Low batteries/bad connections have been known to do really strange things.
The click you hear sounds like the fuel pump relay kicking or trying to kick on. The booster charger may have enough current to run the starter but may not have enough for the starter and fuel pump.
When the charger/booster is connected, and the key is in the 'run' position, the fuel gauge shows no fuel? (dumb question I know) Are you out of gas?