My Galaxy Mini powers on, but then hangs on the "Samsung Galaxy Mini" splash screen.
How can I re-install Android, or get it booting again?
You can fix it manly two ways. Performing a factory reset via stock recovery or flash stock firmware. Resetting is the easiest method. Press and hold power button, home and volume up keys until you see the Android robot logo. Stock recovery doesn't work touch screen you can use volume keys for navigation and power button /home key for selection.
Once you're in the recovery go to the "wipe user data" option via volume key and select that option via power key. Next choose "Yes" option.
Once it's complete you can reboot the phone via stock recovery. In recovery main menu choose "reboot" and select "yes".
Just found that solution and it worked for me! http://howtorootmobile.com/stuck-in-android-boot-loop-tips-to-fix-recover-from-boot-loop/
FYI my phone is not rooted, so I followed the first solution.