Dead battery and no TV out cable shipped.

80% is typically what the percentage reads when the contacts aren't perfect. Take a tissue paper, fold it, and place it between the cover and the battery to try and push it into place a little bit more. Maybe it won't help, but maybe it will.
I don't know where to get 5a version ? pls advise.

One symptom I found with this battery is my pandora will be rebooting by itself in random duration, but with the other battery, it just works fine.
Please check the datecode on the batteries:

If it says "3910", then it's a new battery. This battery is a bit thinner and only works when the battery compartment is padded (the new units have pads already in there).

The old battery should work in all battery compartments with or without padding.
Ya like everyone else says, this really sounds like a contact issue, Just throw some folded paper or something right between the battery and the lid, over where the contacts are. Should solve everything.
you can go to a home improvement store and try some of those self-adhesive felt pads that go below chairs and other furniture to prevent scratching floors.

they sell those in tiny packs for $3 to $5.
^^ Or if your feeling rather ghetto, i think a razer blade is about the right thickness too :p .