2000 crown victoria just clicks after shutting off

hi u doing i hope u guys can help i have a 2000 crown victoria police interceptor my problems began even before replacing the starter an battery so both are new the alternator tested fine. my problem is when i start the car an drive it for a while on certain days after shutting the car off an triying to start again it just does the fast cliking noise like it has no power. but if i wait a while it starts again an fuses look ok what else should i be looking at what can be the problem:runaround:

battery cables and connections.

i cleaned the cables to the starter an to the battery an battery post an still does the same thing