Question Verizon: Bootloop on different ROMs and "Please wait for activation"

Hi there,

I got some strange behaviour on my LG G2. First of all: I bought it on eBay, so I don't know what happens before to the device.

There are a few strange things:

1. The phone reboots randomly about every 2 oder 3 minutes. This also appears on custom roms (installation of those is very hard due to the reboots while pushing files via adb)
2. On stock firmware (Verizon 11A, it came with it and I flashed it several times with kdz und tot method) in the first screen of the Setup-Wizard I have to choose the language. If I click "next" (regardless which language was choosen), the phone says "Please wait for activation" and nothing else happens (can be for several minutes until (1.) appears.
If I avoid this Setup-Wizard-Screen (by pressing vol-up, vol-down und back I may enter the other steps of the Setup-Wizard
3. If phone gets to sleep and I wake it up via knock-on, the device seems active (touch input leads to vibration), but the screen stays black. I got to reboot it in this case (or I wait until it does it by itself).
4. If I connect to a wifi-network and the connection is established, it says: "Temporarily avoiding poor connection" but the signal strength is on "excellent".
5. On some on-times (between the reboots) it may be that some functions do not work as aspected. As example switching wifi on leads to an "Error"
6. Power of or reboot via software doesn't work (phone stucks on "Powering of...") - I may just reset by hardware buttons (vol-down and power).
Points 3-6 are occuring on all tested roms (offical and custom)

Etc.

What could the problem be?
Is there a way to fix it?

Thank you!