So I have some good and bad news. The good news is that you will be able to hack your console. The bad news is that you will not be able to use the CFW that comes with the SX Core because SX OS does not support any firmware higher than 11.0. The caveat is that Atmosphere supports even the latest firmware. If you want a guide, I recommend following this one. However are you sure that your console is patched? Just because it fails the test doesn't mean its patched because there are other factors that can make the exploit fail such as USB port, cable, or even OS.
Thank you, Draxzelex.
I can surely give it another go with my new PC. D you know what guide can I follow? Also, do I still need a "jig" to enter RCM? I think I lost the one I got back in the day.
Thanks again.