HTC Sensation won't boot but vibrates regularly Recently my nice old HTC Sensation broke. Only 1-2 few weeks later, when I had a new one already, I managed to resurrect it by just using a different back cover. Since I didn't find the particular symptoms anywhere else on the internet, I decided to post the problem here and to answer it myself so that it might help anybody to recover his data when seeing similar symptoms.

History of my HTC Sensation:
16 months ago, it got wet in the rain and stopped working for at least some days. I guess this is relevant because the contacts probably started corroding then. I bought another broken phone of the same model, hoping I could replace some parts, but two weeks later, when I came around to do that, it worked again.
This year, the phone more and more often suddenly rebooted, and about two weeks ago, it was stuck in a frozen state where the system buttons below the display were lit but the power button wouldn't work, so I had to remove the battery in order to reboot it.
This happened once more and this time, after connecting the charging cable, reinserting the battery, and powering on it did nothing but vibrating in regular intervals: it vibrated every 18.4 seconds but the display stayed black. Again, this could only be stopped by removing the battery. I brushed the contacts a little and the next time it booted fine.
One day later this happened again and this time no brushing helped. At that time I haven't tried recovery mode since I didn't know about it yet.
So I was sure this is a hardware problem and the phone is predestined to die finally soon, but what can I do now to make it boot at least once more so that I can backup or transfer my data to another phone? Brush the contacts even harder?
1-2 weeks later, I wanted to rescue my data, but again it went into the vibration loop. I replaced the back cover with the one from the other broken device I mentioned above and this helped. Once it booted with the replacement back cover, I tried to reproduce the problem with the original back cover but now it boots ok with that, too.
Anyway, the conclusion is that the phone isn't completely lost when this vibration loop occurs.