First of all, you have too boot rescue or live mode to mount your root partition.
You can boot into rescue mode over serial console with following boot parameters of Debian Jessie installation (press H to go Help mode first):
rescue vga=off console=ttyS0,115200n8
Follow the steps and when rescue mode setup finished, select "Execute shell" option. It asks what is your root device and if it can find a root filesystem on it, a shell will be prepared for you within a chrooted environment.
This is the place where your actual root filesystem was. Open
/etc/default/grub and make sure that
GRUB_CMDLINE_LINUX doesn't have options like that:
If such an option exists (yes, it sounds seem strange because we already booted with this parameter, but grub has some problems with), remove
vga=off part from it and run following command:
After reboot, you'll see a normal boot process.