I have recently purchased this vehicle and installed new battery. The battery goes flat overnight. There does not appear to be a short. There is a potential difference of 13.04V, but there doesn't appear to be any measurable resistance. I've tried removing all fuses, disconnected the alternator and checked resistance with the fusible links removed.

My thoughts..........if the new battery has removable caps, then remove the caps to check to see if the battery is full of water. I have bought batteries in the past that were low on water when brand new.

 

Also, check the output of the alternator. I always have this done at an auto parts store, where a counter man will bring his testing unit out to the parking lot to test the alternator and battery at NO cost. Chain parts stores like AutoZone, and Advance Auto parts will do this.

 

Not sure what you mean by potential difference of 13.04 volts?? Is this alternator output?? If so, that is too low.

A battery going dead overnight indicates some form of load on it. 

 

The test is to get it charged up 100% - which may take over  24 hours. You cannot quick charge one effectively, and repeatedly doing it will damage the plates in it. Once fully charged, monitor it for 24 hours unconnected to the car. If it hasn't gone down, the car is the problem. There is a short and it's draining the battery. 

 

If it does go down, the battery is defective and should be replaced under warranty. It's a pretty simple test and most vendors won't argue the point much, they should just replace it. But - the second battery showing the same symptoms definitely will be considered innocent and the car very suspect. 

 

So far the one thing that wasn't described was getting the battery fully charged (at least 24 hours at 10 amps) and leaving it disconnected overnight to prove whether it's at fault or not. 

Normal current draw on the battery should be around 15-20 milliamps when the car is parked and things have gone into the sleep mode. If you don't already have a meter to measure current with then I suggest you purchase one so you can check the draw on the battery.