When i closed door it does not auto lock by itself

Check debris in the key fob. Over time, dust and dirt may be causing the circuitry to track/short out and implement odd functions.

You must have a "After Market Alarm" or something similar. The factory Auto door lock system doesn't lock the doors until the vehicle reaches 18 mph approximately.
So what I am saying is the Add-On Door Lock/Alarm System is malfunctioning - however some of those aftermarket systems can be programmed to lock doors with the engine running and Driver's door closed (they assume you will be sitting in the driver's seat at that time) It varies depending on which manufacturer built the system. I have seen on some of those systems they provide a small loopwire on the Module that can be cut to disable the Auto Door Lock feature - you might need the install manual to know which one.

I unlocked all doors, trans in park and it seemed to stay shut.

It looks as if you may have to go back to the dark-ages and forget the remote key options, pull the door locking fuse, go back to the old manual way, the key in getting into it. Be ready to spend a few bucks to repair the driver's switching, remote module. Find a local auto-electric business.

if you talking about door latch wont let door close.try to reset all door locks.first if you cant get door close.work unlock button with remote or door switch.then hold open door handle while you flat screw driver pull up latch in door latch should stay up so door will close.once get door close.try resetting all door locks by sitting inside vechicle with all doors close.remove key from ignition.open drivers door.wait 24 seconds.turn ignition switch on and back to lock position 3 times.press and release drivers door courtesy light 3 times.ensure doors lock and unlock.if not wait 40 seconds and repeat procedure.if this procedure fails. you have problem in the door latch and lock mechanism inside the door itself.

You can change auto door locks option in personal settings on the dash tacho button. If you don't have that option you can change them manually by getting in the car and closing all doors, put key into ignition and turn key from "lock" to "on" four times ending in the lock position, then press the power door lock button on drivers side door and then you should hear a chime to confirm the change.

The owner's manual for your Discovery clearly states that this is a design feature to keep you from locking the keys in the vehicle. The doors must be locked with either the remote keyless entry transmitter, or with the key itself.

check your owners manual, i know my car would do such a similar thing all i done was look in the manual and it told me how to disable the autolock feature. if you disable this you will still have use of your keyless entry but it sould diable the auto locking. hope this helps

Either the wring going to that motor or the motor itself is bad.

Do you have the remote programmed for the auto up and auto down on the windows if you hold the remote button?

I don't have that...but have heard that feature tends to cause problems like that.

Is the alarm sound muffled?