Finally I have restored my database, as I bought a SATA cable. Sorry for the radio silence, I hope your readers won't overflow!
#postmortem TL;DR: tried to disassemble my server, fried the BIOS, too lazy to bring it to service center and all my data was locked up on a HDD to which I couldn't connect. But I bought a SATA cable and heroically retrieved the database.
Even shorter TL;DR: you need a backup off-site. I'll probably set up a cron job that will send the DB dump to a remote server.