96 rav4 possible grounding issue

Recently I just had to have my engine replaced. The installation seemed to have gone without incident. The mechanic rode the car around after he was done. Nothing came up. few days later I come to pick up the car and it would not start. Several jump attempts start the car, but soon after it dies. Testing the battery shows it will not keep a charge. Auto zone checks it again and replaces it because it will not hold a charge. Car starts up off the bat with the new battery. I drive home the 15 miles. few hours later I run down to Taco Bell, maybe a mile or two round trip, to grab a bite to eat. Next morning car battery is dead.

Facts:
*First battery was bought in Feb07
*Second battery was dead within 15 hours of installation
*Battery cable leads were replaced in Feb07
*The first jump attempts with the first battery required charging up before the jump then shortly after the car died.
*Hooking it up to two different test stands showed the battery would no longer hold a charge.
*Second battery was dead within 15hrs, but both crank attempts the day before had no issues and were 3-4 hours apart.

Possible causes?

1. alternator
2. bad batteries to start
3. grounding issue?

my question is what opinions of cause are out there? What could be done to check for these different faults such as where in the wiring could I check to see if its grounded properly and where are common places it might ground unexpected?

sound like there is a small draw on the battery, from what i dont know. This is where i would start .First you will need a DMM (digital multimeter) set to test amps disconect the pos. side of  the battery and complete the circuit with the DMM. make sure all doors are closed car is off and any other electrical device are not hooked up like phone chargers or any thing else befor you do this. Now i dont know what the rav4 resting current draw is  but with a little searching or a call to toyota you may be able to find out. any thing above the acceptable draw is not good and if you battery goes dead in 15hrs i would say it will be a bit over. figure that out and i will help you narrow down what is causing it. if no extra current draw is present than we will look at some of the othe possable causes, but i think it will be much faster and less of a headache to take your back to the shop that swaped you motor and have the fix the problem, if you feel thay are not competent or thay say its not there problem id find a nother shop couse this could get a little over the head of a novice.

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bring back the rotary phone so i dont have to press 1 to proceed in english