'96 completely dead

Lights turned on and door open chime sounded with key in ignition. As soon as I turn the key to start car goes dead, and lights do not turn on, no chimes etc.

Replaced battery which did not fix problem.

Sounds like something electical. I would take it to a honda/acura dealer or a mechanic, they should be able to do some tests and find out the problem in no time. I'm sure a they would be a lot more helpful than one of us would be in this situation.

Do you have a volt meter? If so, play around with the battery and turning the car on and off. thats how I fixed my friends car. It may be the alternator. Did the car start up at all when you put the new battery in? Its about $50 to have a mechanic look at it, and over that to replace anything, so have it looked at before replacing things, if you dont know what you are doing.