Why will my changer not make a good connection

Take it back to where you bought it from and have it replaced.

Dead battery. If you haven't charged it for several years it dies.
Unreparable although if you call kindle customer support they may give you a discounted price on a new or refurbished current model Kindle. They'll want your old one for parts.

For the one that is not charging. Is it where it cannot hold a charge or won't make a connection all? Could be a bad battery, or could be the charge port is bent or disconnected. The white screen sounds like it has crashed and won't boot up with its "Operating System" You could try doing a hard reset on the white screen, if that does not fix it then I say it is gone for good and you would need a new one.

thy a second power socket in your hope, try reset the phone disconnect switch off and back on or remove battery and replace before connecting it back onto the charger. then let it charge up for a couple of hours before switching it on again.

It needs a new battery.

It's time for a new battery.

Acer Iconia Tab A500 mfg. 2011, now 11 year old.
the battery is now end of life, called BAD
replace it.
11 year old batteries are no good now.

If the cell phone battery is more than 3 - 4 years old then the battery could be worn out. Rechargeable batteries have a finite number of charge and discharge cycles and will lose their charge capacity over time, i.e. won't charge to 100% and gradually the charge reduces until the battery won't charge up at all. OR The battery shows a 100% charge but when the adapter is disconnected the battery drops off to zero capacity in a very short time. If the battery drops to an unacceptable charge level then the battery needs to be replaced. Rechargeable batteries will fail if stored in a discharged state for long periods.

Ifthe laptop battery is more than 3 - 4 years old then the battery could be wornout. Rechargeable batteries have a finite number of charge and discharge cyclesand will lose their charge capacity over time, i.e. won't charge to 100% andgradually the charge reduces until the battery won't charge up atall. ORThe battery shows a 100% charge but when the adapter is disconnected thebattery drops off to zero capacity in a very short time. Ifthe battery drops to an unacceptable charge level then the battery needs to bereplaced.

If the laptop battery is more than 3 - 4 years old then the battery could be worn out. Rechargeable batteries have a finite number of charge and discharge cycles and will lose their charge capacity over time, i.e. won't charge to 100% and gradually the charge reduces until the battery won't charge up at all.
OR The battery shows a 100% charge but when the adapter is disconnected the battery drops off to zero capacity in a very short time.
If the battery drops to an unacceptable charge level then the battery needs to be replaced