Thinkpad T420s rebooted out of a sudden, freezed and doesn't boot now

I bought a used T420s about 4 years ago. I used it for about 2 years but then the following started:

1. It rebooted out of a sudden after a while (half an hour to hours).
2. At startup all lights flash, power and BT LEDs go on for 3 seconds then they go out.
3. After 5 seconds of darkness it restarts at 2.

And this goes on indefinitely as long as AC is connected, the battery is not empty or removed. Only after leaving it switched off for a certain time (hours? days? I didn't realize a pattern.) it started properly again but the cycle mentioned above happened almost all the time after a while.

Due to this I left it alone for about one and a half a year. Now I tried to reactivate it recently. It started properly but after about an hour the screen froze (a new so far unknown effect) and it didn't accept any mouse or keyboard input.

I always had thought of a heat problem since this started to happen and this time I took the time to open it, clean it and apply fresh thermal paste. To no avail. When switching on the 2.-3. cycle starts immediately, no matter how long (hours to days) I leave it switched off.