The actual problem is, your server fails to mount its root filesystem. The kernel panic error message is just a consequence of that.
You said you don't have console access - then how are you getting these error messages? ("No console access" with servers typically means something like "the server is locked away in a server room somewhere and I can not get at it physically or by any sort of remote console access system." If you mean "the console is non-responsive", well, that can be expected after a kernel panic.)
If you have access to the bootloader, in some distributions (RHEL 7 and newer, most modern Debian-related systems) there is a boot option that will give you access to an "emergency shell". If that is not possible for your distribution of choice, then you'll need to boot from the installation media and select "rescue mode" or similar in the bootloader.