I had the black screen problem last week on my 1039 1st gen. Up till then it was running great. I put it on charge over night but it was totally dead. I thought it was bricked.
Here's what I did to fix it. Similar to what other people have said.
1, Connect it to your PC via USB, I was surprised when the screen lit up after 5 minutes with the battery icon showing 0% charge.
2, After another 5 minutes I pressed power and volume down for 2 minutes then released the buttons and I was in the bootloader. Then I cleared the cache and selected reboot however the screen went black again.
3, After another 5 minutes the boot logo appeared! Then another black screen, damn.
4, Then the boot logo appeared again and it booted! Immediately there was a message saying low battery but when I checked in settings there was 2% charge.
5, I left the phone connected to the PC for a while and when I checked it was on 7% charge. I then connected it to an old Palm 2amp charger and left it overnight.
This morning it was fully charged and I'm using it again.
What I think happened was I downloaded a walking app that monitors brisk walking with GPS. I enabled it for a walk but never turned it off and I think it ran the battery right down to 0%. The normal charger hasn't got enough power to kickstart the battery but by connecting it to the PC there's enough to get it charging again then the normal charger can take over again.
I hope this helps, good luck.