fresh install of 18.04 won't boot

[frankdn01]

Solved! ...well not really.

Thank you both for helping me through this! I don't really know why it worked, but here's what I did:
First, as I reported above, after booting the DVD in 'try linux' mode, I ran fdisk -lu on the hard disk I've been trying to install to:

root@pc:/home/self# fdisk -ls
Device Start End Sectors Size Type
/dev/sda1 2048 1050623 1048576 512M EFI System
/dev/sda2 1050624 488396799 487346176 232.4G Linux filesystem

Grub rescue> ls produced:
(hd0) (hd0,gpt2) (hd0,gpt1)

where gpt2 was sda2.

This AM I rebooted the DVD in 'try' mode again, and ran gparted on /dev/sda. I deleted both partitions and then executed 'install'. Result:
root@pc:/home/self# fdisk -lu
Device Boot Start End Sectors Size Id Type
/dev/sda1 * 2048 488396799 488394752 232.9G 83 Linux

Restarting, Ubuntu 18.04 booted on /dev/sda and is running as I type this. If anyone can explain why this worked I'd be grateful for the education. But as of now I'm a happy camper.

Incidentally this all started when I upgraded to 20.04, to discover that an app I use a lot (gourmet) isn't supported. Naive me trying to work around that broke 20.04 and here I finally am.

[oldfred]

Since now you do not have an ESP - efi system partition, it looks like you reinstalled in BIOS boot mode.

How you boot live installer UEFI or BIOS, is then how it installs.
With UEFI hardware usually better to use UEFI, but some early UEFI have had issues and BIOS then often was easier.