I see. Well, that can be quite tricky. I am not sure whether with mounts Plesk will start, because the operating system that your data center loads via network interface is not the same like the one your fixed installation on the server has. I can outline the steps to gain "maximum" access through a rescue mode system, but the individual steps will depend on your exact configuration, e.g. your partitions etc. So this here can only be an example:
1) Login to rescue system with Linux shell.
2) Then see the available devices:
# ls /dev/[hsv]d[a-z]*[0-9]*
Result could be something like
/dev/sda2 /dev/sda3 /dev/sda4 /dev/sd5
3) Now check which of these is the Linux root / partition (it is /dev/sda4). Mount that partition. We might also need the boot partition if we want to do anything on that, so mount that, too, for example this could be something likke:
# cd /
# mount -t ext4 /dev/sda4 /mnt
# mount -t proc proc /mnt/proc
# mount -t sysfs sys /mnt/sys
# mount -t ext3 /dev/sda2 /mnt/boot
(Again, these are just examples. What you actually mount, what file system etc. depends entirely on your own system. If unsure on the file system type, look it up in /etc/fstab. If unsure about which sda has which content, look it up in fdisk -l.)
4) We normally won’t need the /home partition, but just in case, for the above example it could be something like
# mount -t ext4 /dev/sda5 /mnt/home
5) Now change into the mounted file system:
# chroot /mnt /bin/sh
6) Only if you need to do anything with GRUB, we need to be sure the /etc/mtab file is up-to-date:
# grep -v rootfs /proc/mounts > /etc/mtab
7) From here, Linux commands of the mounted file system should be available.
BUT: When you have changed file permissions on the files, chances are that you won't be able to do much more on the mounted file system, because it will behave just as problematic as the file permissions were set in error.
8) Once you are done, to finish the session:
# exit
# umount /mnt/boot
# umount /mnt/{proc,sys}
(If you mounted other partitions, use them accordingly as the umount parameter.)
A better approach could be to simply wipe and reinstall the system and restore the Plesk content, e.g. websites, databases, email, from a remote backup that you hopefully did.