Anna I would suggest that you first clean your device. Use this [http://www.ifixit.com/Wiki/Electronics_Water_Damage|as your guide.] After that, re-evaluate your phone. you can try a restore by downloading PC SUIT from [http://www.sonyericsson.com/cws/support/mobilephones/start/xperiax10?cc=gb&lc=en|here]
install it, start the Software
Press Tools
Press Phone repair
Press Continue
Wait for PC Suit to download the file
Follow the prompts and select Model X10
Connect your phone while holding the back button and plug the USB cord in. Let the drivers install wan wait while it completes.
Again this may or may not work. I am really more leaning toward you needing a new LCD due to the water damage. But follow the steps anyway. You can download the compete service manual [http://www.keepandshare.com/doc/3293511/sony-ericsson-xperia-x10-service-manual-rar-november-22-2011-9-08-am-28-6-meg?da=y|from here.] Hope this helps and gets you started in the right direction. Good Luck