Thank you for your help.
The charger cable I have seems to be working. I have two wall chargers, one USB charger, and one USB data cable. All four cables, when plugged into the phone, cause the keyboard to light up.
I also have three batteries. One is a very old, well used battery. One is a very old official SE battery that was in its case for the past... 10+ years, and I recently started using it. The third is a battery I recently purchased, hoping it would fix these issues.
The USB data cable I have is not giving a response in my device manager. I suspect the cable might not be working properly. I am really struggling to find a USB cable that will ship to me in Hawaii for a reasonable cost. The usb power cables are as little as $1, but I cannot find a cheap data cable since the device is so old. There are a few in The UK, but with shipping it's over $20. It's puzzling because the USB data cable is in excellent condition.
Do you know if the DCU-60 cable will work? They are much easier to find.
Here is a short video of what the batteries do when plugged in for five minutes:
All three batteries first light up the keyboard (dimly), then light up brighter, and the red light comes on. Only one battery so far is doing the blinking thing. The other two batteries, the lights are solid. No blinking. holding down POWER causes the red light to go away. The phone vibrates once, and there is no charge to the keyboard lights or to the screen. It stays black.
As you can see, the buttons are falling off (My w580i is even worse). The phone was well cared for, but the adhesive gave out after 15 years. Oh well.
With my "new" battery, I am getting a red blinking but it's slower. Also, every five minutes when I check it, the rate that it blinks seems to be different. faster sometimes, slower. very odd.
Thank you. Sorry again for my late reply.