Dead GA 628
 

My GA628 is still a virgin. I have never tampered with it or
changed any of the software.

The problem is that it shuts down shortly after startup.
This only happens when there's a SIM inserted. Without
a SIM it just displays InsertCard until the battery
runs out.

I thought it was a battery problem so I try another one.
Same thing... Well, maybe they're both bad, so I try with
the charger. Same thing!

What's the problem?!

Another weird thing:
When I suspected the batteries I thought they were
suffering from the famous memory-effect known to occur
on old NiMH battery packs. So I connected the battery to
a tiny light bulb and left it there until the light went out.
I was certain that the battery was completely empty, but
when I attached it to the phone and connected the charger,
the charge indicator started at two (out of four) marks.

Btw, the battery connectors were replaced a long time
ago by a "pro".

check screws, both upper, they are used like battery connector, maybe stupid, but...
And old battery can have enough volts fol a lamp, but not enough power for phone...low current. An common problem on batterys for these phones is bad soldered cells inside of batery pack, you need to open battery to check it

But if that was the problem, the phone wouldn't die when
I had the charger connected (?).

And you're right: A lamp requires less power than a phone,
so when the lamp died I was certain the battery was empty.