Starting Problems -Ignition ?, Grounds?

I have a 87 caprice, and it has 93000 original miles on it. I have replaced alot of thing on it, but recently I have been having problems with starting it. I'll go to start it (sometimes it works sometimes it doesn't)
And it will have power in the ON position, and ACC. But as soon as I go and turn the key. NOthing. Like the starters bad or something. But I have replaced:


Starter
Plugs
Battery
And I just had the Alternator & Regulator tested -ok
Batter - ok
I do have a CD player in it and 2 amps.
Do you think that those turning on when I turn the key to On have something to do with it?

Help!

I would check you ground(s) and your +..... If trouble is worse when its hot then leads to ground- as heat increases so with ohms. Check your neg to batter and your neg to engine as well as to body. I am assuming you will know how if not let me know I will post some how to's and what readings you should see to a couple spots. Also could be the switch but that may not follow temp. Good luck
Flip