Fuel System and Dead Battery

sounds like a parasitic draw test is warranted. To do this without the use of a multi meter and you suspect it is the fuel delivery aspect causing the short. disconnect the negitive battery cable and with the use of a 12v test light connect it inline by connecting the clip end to the post and the probe end to the cable removed. any draw of electric will cause the light to illuminate. You may have to also pull fuses that normally draw power when the vehicle is not in use or key is not in ignition such as dome light, cigarette lighter and radio. If the light is still lit pull the fuel relay and see if the light goes out. If it doesn't it may not be the fuel system causing the short draw. Pull one fuse at a time until the light goes out and that is the circuit causing the short or battery draw.

Stuck fuel relay is a known issue with some years of the town and country. My 2012 has it. There was a recall and a fix for older models but it did not cover mine. Nonetheless, I did a websearch and found a couple videos of how to work around the problem. Applied my work around in 5 mins. Not sure if allowed to post a link in here...but you can find it.