Did you verify the old battery is actually depleted by measuring the voltage with a voltmeter?
Symptoms of bad solder connections on the circuit board can give "unreliable lock/unlock operation" (but with reliable led blinking on the key fob itself), which can easily trick casual observer into thinking it must be a weak battery or poor antenna or something (all the wrong conclusion when the solder joints just need to be reflowed to restore reliable lock/unlock operation).
I'll bet if you actually measure the voltage of your week old battery, you'll find that it's still good. But - please let me know if I'm wrong. Best of luck!
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