The password is your BlackBerry ID password?
You say you deleted "it".... Exactly what did you do?
I don't know why BBM is asking for a password, except if you had not successfully logged in at the start with your BlackBerry ID.
You will need to sort out the issue with your BlackBerry ID, but you'll need to figure out first exactly what the problem is. Have you forgotten your Password? Are you absolutely sure you are using the correct username (an email address) and password? For what it's worth, see How to regain access to your BBID - BlackBerry Support Community Forums
It's possible there is just a hiccup in the system. Try logging in to BlackBerry ID online using a computer to verify that you are using the correct credentials. You could try rebooting the device or doing a soft reset if rebooting doesn't correct things. Do do a soft reset, either hold the power button down for 10 or 15 seconds until the device reboots and you see the red LED, or hold down both volume button until the device reboots.
If you have fogotten the BlackBerry ID and can't recover it, then you will need to create a new one and start over.
So, straighten out things with BlackBerry ID and then see where you stand. There are other things that could be going on (I'm thinking APN for one). But one thing at a time.