It is the digitizer (device that convert touch inputs to signals) that has damaged. You will have to replace the entire screen, but none of the files or data on the phone will be affected. The memory is still safe so thus your contacts. You have to send it to Samsung to replace the screen. And make sure to tell them not to erase or factory reset the phone.
Now, you can't activate or get to the contacts without using the screen unfortunately. But if you've setup your Gmail account on it, then there is a chance that the contacts were backed to Gmail. To check it, on your computer goto www.gmail.com and login with your username and password.
Then in Gmail, click the Gmail link under Google in the left side and select Contacts. All the contacts that were synced to Gmail will be displayed there. These contacts will be transfered automatically to any phone that you register with that Gmail address.
Another option to backup contacts is through your PC. On your PC, download and install the Samsung Kies application from here ---> http://www.samsung.com/in/support/usefulsoftware/KIES/
Open Kies and connect your phone to your PC with the USB cable. Kies will recognize it. Then click on Backup/Restore tab and click Backup. This will backup the entire phone to your PC. You can restore this backup to any phone you want.
If you have any questions or would like any additional information, please don't hesitate to ask. I would greatly appreciate if you take a second to rate my service positively.