Chevrolet Repair: 1977 corvette, carburetor issues, float bowl

Question
I have a 1977 vette, It has a new carb and fuel pump and the timing is set correctly, The problem is when it starts from a cold start, I have to pump it till she fires, It rolls over about 15 times before starting, Once started it stars fine after that.  What the real problem is that when I kick it will bogs out when the 4 barrel come in and it shifts gears. As soon as I leave off on the gas, it hesitates, then I am able to run the car but it has no power.

Answer
HI JIM THIS IS ALL CARBURETOR ISSUES FOR SURE.THIS IS A GM QUADRAJET YES....THE COLD STARTING PROBLEM IS THE FLOAT BOWL IS BLEEDING OUT OF FUEL OVER NIGHT AND THERE IS NO FUEL IN THE BOWL WHEN YOU TRY AND START IT...IT NEEDS TO BE FILLED WITH FUEL THEN IT FIRES. THIS IS BECAUSE THE FLOAT BASE BECOMES PORIOUS OVER TIME... WHEN I REBUILD THESE CARBS I FILL THIS SECTION WITH EPOXY..COMMON PROBLEM...THE BOGGING OUT WHEN YOU HIT THE THROTTLE IS THE BACK 2 SECTIONS OF THE CARB SECONDARIES ARE COMING IN TO FAST CAUSING A BOG..THERE IS A  ADJUSTMENT FOR THIS. THERE IS A ALLEN HEAD SCREW ON THE PASS SIDE REAR SECTION OF CARB THAT YOU WILL NEED TO SET SO THE SECONDARY TOP PLATE OF CARB DOES NOT OPEN SO FAST..TIGHTEN IT UP A TOUCH..THIS ALLEN HEAD SCREW IN UNDER THE SIDE PLATE POINTING UP.GET A MIRROR YOU WILL SEE IT.DO NOT REMOVE THE CARB FOR THIS.. THIS ALSO MAY HAVE A LOW FLOAT LEVEL THAT WILL ALSO CAUSE A BOGGING OUT..IF THIS CARB IS NEW I WOULD RETURN IT. IF REBUILT UNIT GOOD LUCK. SOMETIMES YOU HAVE TO GET 3 CARBS TO GET A GOOD ONE...YOURS CAN BE SET BUT YOU MAY NEED TO OPEN IT UP TO DO SO...LET ME KNOW HOW THIS GOES AND GOOD LUCK TO YOU,,,TOM