Boot into recovery mode, and connect your device to your computer; then mount your device's internal memory/SD card and download the corresponding firmware for your device (ensuring that you have the correct firmware, or you will brick your device!).
After this, flash the firmware via the recovery, bearing in mind that it will wipe the current version of Android from the device.
Samsung devices are usually very good, as they keep personal data such as music and photos separate from the system partition, and so your personal data should remain intact. With this in mind, attempt to back-up your device first (your recovery function may have the ability to do this).
Try and establish a connection with ADB using the ramdump mode (usually Volume Down+Power+Home), and it may work.
Otherwise, ADB requires a fully functioning device to work (for security reasons).
Before installing something that modifies the way your device works (such as Chainfire's mods, Beats' sound driver, etc), always back-up your device first! Only you can be blamed for not taking a backup before you installed the mod.