F-350 Super Duty Lariat 6.0L Turbo Diesel

• Automatic transmission
• 77,000 miles

I bought this 2003 Ford F350 Turbo Diesel truck from a dealer a little over a month ago; it worked fine up until one day last week. I got home from work I turned off the truck to open my gate and it would not start. It cranked a few times then it seemed like the batteries (2) started to go down. I checked the oil level and it was ok. I check all the fuses and they were all ok also. I have a BullyDog Programmer installed and set to tow/economy, so set the truck back to its stock settings and tried to start it and it started. I pulled into the yard and restarted it and it again started ok. I left it overnight and the next morning when I tried to start it, it seemed like the batteries did not have enough power to start it. I checked the Voltage which read 11.48 volts. I charged 1 battery and I noticed that the terminal was dirty so I cleaned it. When I reinstalled the battery it started ok. I didn’t drive it for about a week. When I got in yesterday afternoon it started ok I drove it around all afternoon turning it on and off with no problem (no weak starts or weak batteries). I activated the alarm and went to bed. This morning when I tried to start it, it was almost unable to crank. Batteries seem to be week again. Seems like something is draining the battery when it is parked.

Does anyone have an idea what could be the problem? No lights or any other accessories were left on. This is becoming a pain… any help would be greatly appreciated.