iHAVE A 2001 cADILLAC dEVILLE THAT HAS A PROBLEM STARTING. Was starting good the

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GOOD THEN IT HAD AN OVERHEATING PROBLEM, WE INSTALLED A NEW WATERPUMP, THERMOSTAT, AND RADIATOR CAP. WE HAD HARD TIME GETTING AIR OUT OF SYSTEM, BUT FINALLY DID. NOT RUNNING HOT ANYMORE. NOW WE HAVE NEW PROBLEM I DON'T WANT TO START RIGHT. cAR WAS STARTING GOOD BUT BEGSN TO RUN A LITTLE ROUGH UNTIL CHOKE WOULD RELEASED. tHEN I GO OUT TO LEAVE AND TRY TO START CAR AND IT JUST GROWLS 1 TIME, NO START. TRIED AGAIN GROWLED 2 TIMES, BUT STARTED UP. SOUNDED LIKE DEAD BATTERY TO ME SO I HAD BATTERY CHECKED AND WAS TOLD BATTERY CHECKED GOOD. CAR STARTED GOOD ALL DAY BUT NEXT MORNING SAME THING HAPPENED SAME WAY. SOUNDS LIKE ALMOST DEAD BATTERY TO ME BUT MECHANIC SAYS BATTERY IS GOOD. What do you think problem is.