Toyota Repair: 2004 Camry. 4cyl loses electric power

Question
Camry  has been trouble free. Lasts  week starter was dragging and slow so put in another battery known to be good. And all was well starter spun fast  , kites brute and indicated charging  by dash lite.  This am  car operated properly.. Later in am car acted nearly dead...starter only clicked and all other electrics acted nearly dead  but enough remained to lite dash indicators however headlines,and horn would not operate.checked some of the fuses. Ok

Acts like battery is dead but battery indicates charged and  batt charger tapers down quickly.
Your ideas to diagnos are appreciated thank you   Art

Answer
It sounds like there may be a charging system issue, try jump starting it, if it starts let it run for a while, if it stops running as soon as the jumper is removed then the alternator is not charging the battery, if you have a volt meter measure the voltage at the battery while the engine is running, it should be close to 14 volts.