Hopefully, you have a Time Machine back up or a clone of your old hard drive using 3rd party cloning software like Carbon Copy Cloner or SuperDuper!
If you don't have a back up, hopefully you created a Mountain Lion installer USB thumb drive to boot from and install ML or you used the OS X Recovery Disk Assistant to create a Mountain Lion Recovery HD on a USB thumb drive so you can boot from that to download/install ML
If you don't have any of the above, hopefully your MBP has the Internet Recovery feature. Restart your MBP and press/hold the COMMAND + R + OPTION keys. Make sure you have a WiFi or ethernet connection. This will boot you into the Apple servers and their Recovery HD for the OS X that came preinstalled on your MBP. Then you can go to Disk Utilities and format your new drive as Mac OS Extended (Journaled) and click the Options button and select the GUID radio button which will format and make your new drive bootable. Last, install OS X.
Otherwise, if your MBP came with Snow Leopard, you will need to boot from the SL DVD (which you say the drive is not working) by restarting and holding the C key. Then you can go to Disk Utilities and format your new drive as Mac OS Extended (Journaled) and click the Options button and select the GUID radio button which will format and make your new drive bootable. Next, install Snow Leopard, go through setup and update SL to 10.6.8. Now you'll have the App Store and you can log into to it using your Apple ID and download/install ML.
Good Luck.