I had a similar issue when I bought my car(used). Replaced the battery in the fob with an unused one, but one that sat in a drawer for a while. Things didn't work and I thought there was a problem with either the fob, or the CA system. As a last resort before getting gouged at the dealer, I went and bought a fresh, new fob battery.. boom, all working and has been for a year now.
So, go buy a fresh new battery for the fob before doing anymore troubleshooting.
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