So, what does is say on the side of the barrel?
If the Federals go into the chambers most of the way but stop about 1/8" short of all the way, you probably have a 38 Special rather than a .357 Magnum (unless a lot of 38s have been shot in the .357 chambers) and the "crud ring" is stopping the cases. Through cleaning will fix that.
I looked at your other posts between the time I posted (#2) and you posted (#3). I see that you are more familiar with centerfire arms than I first thought and would certainly know the difference between the 22s and the centerfires.
Do the casings go in partway or can they not get in at all?