Shut down the corrupted database and make a physical backup of it.
I did it before trying anything.
Check the disks and memory on the machine where the problem occurred.
We are using virtual machines (VMWare). I will ask then to investigate anyway.
You can try to salvage data from the corrupted tables, either using "zero_damaged_pages" (but that will only work if the page header is corrupted), or by excluding problematic tuples by their "ctid".