What was the voltage of the battery that you installed when you tryed to start the vehicle after it sat for a while???? Diconnect the negeative battery cable and let it sit for a little while until all the computers and such go to sleep. I would guess about 20 minutes, using a voltmeter attach on lead to the battery cable and one lead to the battery post and see what kind of draw you have. IF it is a high draw then start removing IP fuses until you find the culpert that causes the high draw.
How many miles on vehicle and has the starter ever been replaced or repaired. I would also check the voltage draw while trying to start the engine. Could be the armature or bruses are bad in the starter.