car starts intermittently. had the battery, alternator and battery cables all on 1996 Acura TL

recently replaced. not sure if I can be specific of when car is hot or cold but first time starts are always reliable. the dashboard lights come on, no problem with the battery, all power works. go to grocery store or shopping get back start. no sound when I try to turn over, no click no grind, nothing, just lights on dashboard wait a few minutes, maybe just open and close hood, get back in and starts right up? could it be starter, solenoid, relay switch, fuel pump switch. please help.

Asked by for the 1996 Acura TL
Starter most likely!.... After you drive it.... Turn engine off and it sits there awhile.... Starter gets 'heat soaked' and will not crank the engine until it cools off a bit.... That's my 'online' guess!!.... This can be confirmed by a mechanic or someone with a good bit of car savvy....
ok, i guess it will eventually have to be replaced, i will let you know what the diagnosis is after i get it checked out. thanks for your prompt online guess, much appreciated~