I'm guessing the issue is that the PS3 isn't responding to your controller input.
Ensure that the PS3 controller is actually on. You can turn on the controller by pressing the Playstation button in the center of the controller. There will be a red light on top of the controller indicating that it is on.
If no light shows up, it's possible that the controller simply has dead batteries. Grab your controller charge cable (should have been included with controller, looks like this
) and connect the controller to the PS3 while the console is on. Give it a few minutes, then press the center Playstation button again and see if it responds.
It's also possible that the controller just isn't synced to your PS3. Again, grab the charge cable and connect it to your PS3 while it's on. Then press the Playstation button while the controller is connected. It should sync it to the PS3.
If none of that is working for you, there may be an issue with the controller itself. The easiest fix it to reset the controller. There should be a tiny button in a hole on the back of the controller. Just press it (you'll need a paperclip or something to do it) and the controller will reset. I believe you'll have to re-sync the controller (using the cable again).
You should also try syncing other controllers to your PS3 to make sure that the issue isn't with the PS3 itself (which would be awful; I've never heard a PS3 breaking like that but I suppose there is always a first). If other controllers work then either your controller's battery is dead or the controller is actually broken. I don't think Sony repairs/replaces controllers so you may have to buy a new one.
It may be worthwhile to checkout their support page first, to see if anything helps before shelling out 50$ for a controller:Sony SupportSony RepairAmazon - PS3 Controllers
(I recommend Silver; it's ****).
Hope it all works out!