I have a 96 honda accord ex 2.7L v6... single *click* noise

SOURCE: 1991 Honda Accord Starting/Ignition trouble

sounds like a bad battery or the battery cables are corroded where they hook up to the battery or loose. if it cranks for a couple seconds slow than clicks quickly there isnt enough voltage getting to the starter. not all new parts are good.

SOURCE: 96 Honda Accord ignition Key problem

I might try checking with the dealer for a recall on this one

SOURCE: 1989 Honda Accord won't crank - starter good - what next?

check powers out of the ignition switch big in big out usually first place to start

SOURCE: 1997 Honda Accord EX wont start then will start

Most of these Accords had two recalls pertaining to the ingnition switch. There is an interlock issue, and an electrical portion of the ignition switch recall. I would start by replacing the electrical portion of the ignition switch as this will most times fix this issue. The clicking noise may indicate an issue with the starter however. Would advise having a starting and charging system test at a professional repair facility to check the starter, but the ignition issue would be where i would start.

SOURCE: where is the starter relay on a 94 Honda Accord

Yes, it sounds like your solenoid is bad and staying engaged against the flywheel, you could do an amperage draw and a voltage drop test to find out for sure, but you will need an DVOM and a amp clamp. Or you could take it into an auto parts store and they will test it for free. Hope this helps.