OK, working with what we have to work with. Not a problem to try !
Graphics is the issue, and that issue is dependent on a graphics driver, that is dependent on what the graphics interface is.
Heads up, if it turns out to be SIS graphics on that old box, you are in for a long hard row to get graphics working.
To get your question of a persistent "nomodeset" one does edit the file /etc/default/grub -> this line: "GRUB_CMDLINE_LINUX_DEFAULT="quiet splash"" and add "nomodeset" @ quiet splash.
OK, here is a thought to get ya booting to a functional terminal to enable us to get relevant hardware information.
Edit that line and remove the terms quiet splash and insert the terms "text and nomodeset" . One then boots to a terminal (TTY1).
Also something else we might be able to do is from the grub boot terminal, find out what graphical modes are supported and also edit the line in /etc/default grub to use that initial resolution (???) -> GRUB_GFXMODE=1600x900 ( where 1600x900 is the highest resolution MY monitor will support, yours will be different !)
To know what modes are supported -> boot grub command line command 'vbeinfo'.
Once completed editing the grub file, as you know, the terminal command
must be issued to propagate the change to the rest of the system control files.
Once we are at a system terminal (TTY1); post back the out put of terminal commands:
To see your graphics card and info.
lspci -nnk | grep -iA3 vga
sudo lshw -C display
let us see what