mysql errors even though these files do exist:

110405 13:21:37  InnoDB: Operating system error number 13 in a file operation.
InnoDB: The error means mysqld does not have the access rights to
InnoDB: the directory.
InnoDB: File name ./ibdata1
InnoDB: File operation call: 'open'.
InnoDB: Cannot continue operation.
110405 13:26:15  InnoDB: Operating system error number 13 in a file operation.
InnoDB: The error means mysqld does not have the access rights to
InnoDB: the directory.
InnoDB: File name ./ibdata1
InnoDB: File operation call: 'open'.
InnoDB: Cannot continue operation.
110405 13:28:50  InnoDB: Operating system error number 13 in a file operation.
InnoDB: The error means mysqld does not have the access rights to
InnoDB: the directory.
InnoDB: File name ./ibdata1
InnoDB: File operation call: 'open'.
InnoDB: Cannot continue operation.

InnoDB: File name ./ibdata1
InnoDB: File operation call: 'open'.
InnoDB: Cannot continue operation.
110405 13:26:15  InnoDB: Operating system error number 13 in a file operation.

I accidentally set all ownership on everything in /var/lib to root.root

This meant that the normal mysql directory now had root ownership, so MySQL could no longer read its own files.

I was getting worried because one by one my databases couldn't be read, I feared the worse (a RAID array corruption), but fortunately it was just an idiotic and simple mistake to fix.

So the "error 13" is correct, that basically the DB lacks permissions to access the relevant files.