We still don't know if mentioned bug is what affects you, because we haven't seen any error messages. If you press Esc after grub menu, in your HP logo boot stage, does it show any error?
Anyway, you need to boot from livecd or liveusb.
If you want to test the mentioned workaround, you'll have to (if I understood it correctly) chroot
into your broken installation and manually update your volume group metadata using vgck --updatemetadata VGubuntu-mate
command. I assume VGubuntu-mate
is your volume group name based on your previous posts.
If you don't want all this, the most straightforward solution will be to boot from livecd or liveusb, mount your logical volume, copy all sensitive data from previous installation, then repartition your disk to a configuration that is more familiar to you (since you have to support this system). Then perform clean install.