I changed the battery on my 1996 Honda Accord LX and now the car won't start. I have power, but the LED on the extreme left of the dashboard blinks 3 times repeatedly, the turn indicator sound clicks and the doors unlock automatically if I try to start. Help!

Do you have a remote door lock? Try clicking your doors open and closed. You can turn the key to the start position three times and re-set the security that way on some Acura/Hondas. My son has had to turn the key to the start position and change the position of the Automatic gear shifter - back and forth. I think it has something to do with the Neutral/Park safety switch on his '93 Legend.
Make sure the ground wire is good. The security and starting circuits depend on a ground wire going to the engine from the battery/transmission area. It may be loose or not getting good contact.
Honda/Acura has kept the old fashion battery post type batteries. Always wire brush the inside of the cable connections and the battery posts.