Cleaning cache isn't enough, boot back into recovery mode again & do a wipe/factory reset. This will obviously wipe the phone.
If that doesn't work or you don't want to do that you only have one other option; get stock firmware for country/carrier from Samfirmware (the 'put the official Jellybean firmware on it' you were talking about) & flash it with Odin (How ? Stickied thread near top of Q&A titled 'Flash stock firmware' has instructions'). If you have problems with Odin/getting a successful flash find Hopper8's 'Odin troubleshooting' thread stickied in the General section & go through as many of the troubleshooting steps as many times as you need to in order to get a successful flash.
If you're lucky, this will fix the problem on its own/without having to do anything else & no data will be lost. But the bootloop may also persist after doing this, and if it does, you'll have no choice but to boot into recovery & do a factory reset. This will more than likely fix the issue though.