Default Flashing new Recovery or PDA, nothing works

My i9250 has a strange problem

If I use ODIN to flash anything on it nothing changes even though it says "PASS".
If I use fastboot to flash a new recovery onto it, it says "OKAY" but when loading recovery the same version as before (v5.x.x.x) is still there even after trying to flash a new one on (v6.0.4.7).

When in recovery and factory resetting it does not produce any errors, but when I try to load up the OS it does not seem to have anything wiped.

I have a problem with my OS where when it just starts and shows the lockscreen after a few seconds it restarts.

I've had experience with other phones like the Galaxy S2 and HTC One X and none of these have produced the same kind of problem, where no matter what I try nothing seems to change on the device itself.

Possibly related information: In cwmrecovery (v5.x.x.x), whenever I push files onto the /sdcard/ through adb they only stay on the /sdcard/ until I power off the phone (then it disappears). Installing update from zip using these files does not result in any change to the device. I tried installing a new cyanogenmod version but after saying "Installation success" or something like that it still proceeds to load up the old version of cyanogenmod, with the same customized background image and lockscreen (and then proceeds to crash in the same manner as before).

I'm extremely confused why nothing I do seems to produce any change, even using ODIN to try repartition the device and install the stock rom and everything. What's wrong with my phone and what can I do to make flashing actually do something?