Step by step, this is what you should do:
Your iPad seems to be in recovery mode. There are two possibilites to exit: restart, or do nothing at all and wait for 15 minutes, without connecting it to the computer.
If this gets your device out of recovery mode (no Apple logo with iTunes sign and cable), you can connect your iPad to the computer and back it up this way:
http://support.apple.com/kb/HT1766
Then use iTunes to restore it to the latest software version.
If you can't get it out of recovery mode, you'll have to use these instructions:
http://support.apple.com/kb/HT1808
If you don't have a recent backup, the data will be gone, sorry!
Btw: recently, the latest iOS is 7.1.2 - this version was released yesterday.