When I let my 2004 Ford F150 set for 2-3 days, the battery goes completly dead. I replaced the battery 2-3 months ago. I can hear a faint humming at the gas filler entrance .

yes whatever the humming noise is could be killing your battery. anything that stays on too long when the vehicle is off can kill it. can you pull the fuel pump fuse and see if the humming goes away?

That same thing happened to me . the eletrical post are loose try tightening them.

If those options did not help check your alternator, when a alternator is going bad it often drains all the life out of a battery in a few days and when it is completely dead will drain it in a minute flat