I have a 2006 Honda Accord Ex-L V6. 122K miles.
I has very recently had a tune-up (plugs and cables), a new battery, and an alternator replaced.

As of recently it has been doing something strange when going to start up. If it sits over night without being driven for a day or so it has trouble firing.
I can put the key in, the engine turns over, but it begins to get slower as if the battery is dead, after a few minutes it doesn't even do that its as if its completely dead, not even a click when the key turns.

If i wait about an hour, it fires right up. its seemingly random, but as I said its getting noticeable after not driving it for a day.

Are there any ideas as to what is going on?

 

when you say it goes completely dead, do the lights on the dash still light up?