New key "theft deterrent system" message

So, key broke off in ignition. My car has a transponder key, so the key has a chip. I purchased a new key, just a basic key and had it matched to the master key. (I was able to get the broken piece out) I then removed the chip from master and tapped it to the new copy. That way I wasn't going to have to mess with reprogramming or the costly steps. But, it didn't work. Car was still showing "theft deterrent system" on display on dashboard. Come to find out, the copy I had made is not an exact match (get what you pay for). If the new key was made correctly, an exact match, with the chip from the master tapped to it, should this trick work? I mean how would the car know it's a different key since the chip from original is what the computer looks for? If it's the same chip, with an exact match of the master, why wouldn't this work? The photo shows the key that I had made at hardware store, and the chip from the master key tapped up right below the plastic. Just really not understanding why I would still need to reprogram a copy of a key if the original chip that's already recognized by my car is technically where the chip should be.