2002 Mustang Gt With New Battery But Won't Start

After getting gas, I tried to turn my car back on and it clicked and did not start. After turning the key off then back on, my gauges and lights worked but went off when I tried to start it again and after that it was totally dead. I took the battery to autozone and some acid had leaked out so I got a new one and it still will not start. I disconnect and reconnect the negative and everything works but as soon as I try to start it, it clicks and nothing works. I've reconnected it probably 3 times and it does the same thing. This is my only car so I'm pretty desperate
 
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When you say "nothing works" do you really mean nothing?

Try this. Turn the head lights on. Are they bright?

What happens to the head lights when you attempt to crank? Do they go out? If so this means that the voltage is dropping too low. The problem has to be:
  • battery
  • battery cables
  • battery terminals
  • grounds around radiator core support
  • starter drawing too much current. If this is suspected, can you turn the motor over by hand?