Ok, I've identified the culprit. Apart from the SSD, my father had two HDDs in the machine. One of them was a 2TB hard drive that used to be his old Windows 7 install. He never removed it after migrating to an SSD... It had bootable flags (bc windows was installed in it), 64k bad sectors in it, and wouldn't even mount in Nautilus (it would as of last week). Once I removed it from the system, the installation went smoothly. Thanks for your help with that.
Now though I am having the issue where booting the system to the default option after the installation (named "ubuntu: SSD Name" in the boot menu) shows a grub screen with a prompt. But if instead I choose the option with just the "SSD Name" in boot options, then it boots up fine. How can I fix that?