CAR WILL START IN Morning BUT IF I GO TO THE.

CAR WILL START IN MORNING BUT IF I GO TO THE STORE TO PICK UP SOMETHING QUICK MINUTES) THE GO TO START IT IT WILL NOT TURN OVER, WILL CRANK. I HAVE TO LET IT SEAT FOR 10-15 MINUTES BEFORE IT STARTS. HAD IT AT TOYOTA THEY CHANGED THE STARTER BUT IT DIDN'T SOLVE THE PROBLEM. THEN LAST KNIGHT I CHANGED THE OIL AND ABOUT AN HOUR LATER WENT TO GO OUT AND IT WOULD NOT START. FINALLY AFTER 5 TRIES IT TURNED OVER BUT WHEN I LET OFF THE GAS IT WOULD DIE. I CHECKED THE THROTTLE CABLES AND THROTTLE LEVER SEEMED LIKE THE LINKAGE WAS STICKING SO I PUT SOME LUB ON THE LINKAGE AND HAD NO PROBLEM STARTING.(SO FAR) CAN IT HAVE ANYTHING TO DO WITH FUEL FILTER OR INJECTION PUMP?