If the phone still works and you don't already have the insurance option on it, my suggestion to you is to add the insurance. Typically the way it works is that as long as you are able to make and receive a phone call AFTER you've added the insurance option, they will honor the insurance claim.
What will happen thenn is that you will be given a certified pre-owned phone as a replacement AND if they are short on Droid X's they may allow you to get a Droid X2 or some other equivalent phone.
I wouldn't waste my time trying to get water damaged repaired...you'll be without your phone and thru the insurance process they will overnight you a replacement.
DS18 had a sensor go out on his original Droid last fall. He brought it to the Verizon store and they tried to fix it but were unable to do so. They replaced it with a refurbished model (he has insurance on his phone) for no extra charge. It took a couple days to get the new one in the mail. He had NOT backed up his phone online and lost most of his apps, etc. so do that before you do anything (backup assistance).
This is good advice, but if the screen is not working it will be difficult to see any of that. Any paid apps will automatically transfer over, any free apps - well hopefully you have a good memory of what they were.
As for backup assistant (VZW app) if you are using GMAIL and Google Contacts - that will be automatically backed up and as soon as you add your GMAIL account to the "replacement/new" phone they will appear - same for Facebook.
The backup assistant actually conflicts with Google contacts and will cause your contacts to get doubled and even tripled up - or try to join contacts that are not the same.
You should only use one or the other...I actually got so frustrated with this at one point that I exported all of my phone contacts to an excel file, cleaned it all up - did a factory reset on my phone to wipe everything out and then added them all thru Google contacts/GMAIL...much cleaner address book now. Some miscues with FACEBOOK contacts trying to deciper some of my contacts like my cousin and uncle for example tha thave the same name...phone will try to join the contacts as a single contact, including their facebook profiles.