my ipad 2 will not charge and is now completely flat. What can I do?

Make sure you're using an original apple ipad charger and plugging into a wall outlet to charge, not computer.

Its possible that the charger is bad and may need replacing.

Its also possible that the battery has gone bad and it may need replacing.

Apple does offer battery replacement, you will have to send to them or take it to an apple store.

http://support.apple.com/kb/index?page=servicefaq&geo=United_States&product=ipad

Before you do that though, I would recommend reading through these links first for some more information on how your battery works, needs to be charged and maintained.

Apple Batteries - iPad

http://www.apple.com/batteries/ipad.html

Apple recommends that once a month you let the iPad fully discharge & then recharge to 100%.

How to Calibrate Your Mac, iPhone, or iPad Battery

http://www.macblend.com/how-to-calibrate-your-mac-iphone-or-ipad-battery/

iPhone, iPod, Using the iPad Charger

http://support.apple.com/kb/HT4327

1. Reset iPad (not applicable)

2. Try another wall socket

3. Try another cable (make sure it's an original Apple cable)

4. Try another charger (make sure it's an original Apple charger)

one last suggestion

Try restoring it via itunes

How to restore

Via itunes

http://support.apple.com/kb/HT1414