That seems really wierd! Well, I'll explain how mine works- If you get out of your car and hit it once it will flash and beep once (Its locked and armed) If you hit it again it will flash and beep twice (This unlocks the driver side door) If you hit it again it flashes three times (This unlocks the passesnger side door also)
I really don't know why you would only want to lock it (without arming) I mean since the alarm only goes off if the door opens, why wouldn't you want your alarm to go off if someone opened the locked door? But, if thats what you want you just lock your doors with the power lock on door.
If you have your door open and hit the button it will have a high pitched squeel until you close the door, then you need to press the buttton again if you want to lock it.
You shouldn't need to hit it fast at all. If you hold the button for 5 seconds (or sometimes press it a lot real fast) it sets off the panic alarm.
Your problem is wierd, this is all I can really tell you. sorry. Maybe someone else will chime in with an answer.
Maybe its in a different "mode" there is a cheafuer (is that spelled right?) mode but I'm not sure how that works. Good Luck!