I cannot understand how putting the end cap on an ego-PT would do anything one way or another. It sounds like the batt is not charged. Have you tried charging
through the USB port on it, and alternatively, charging like a normal ego, which an ego charger? It is possible that it is faulty and not actually charged when it says it is (the red light on the USB end goes out). I have had several USB-batts, including an ego-USB and a Sit-n-Go USB, and the charging port always seems to be the weak link...it either does work at all, and the batt is returned, or it stops USB charging after some weeks. Charging with the regular batt charger will tell you if this has happened to yours.
And I always end up misplacing the cap. It is not needed other than for looks. My ego-USB is always in my car, either plugged in or not, and I don't use the cap. It should not be affecting the operations at all. If this one is new, I would see about contacting the vendor and getting it replaced.