I would try a distro that doesn't use Plymouth by default.
All Ubuntu Family members are more resource hungry than most other distros using the same DE.
Try a couple of these. First link is for 32bit, second for 64bit.
I would recommend the ISO for Xfce. I think it may run on that much ram. I know it runs on 512. Will not have any or the many added Gnome packages included with Xubuntu. Just straight up Xfce4.8.
If you are a Lubuntu fan you will be disappointed with Lxde DE. Lubuntu is the nicest preconfigured Lxde you will find. I am not a fan of the Ubuntu family at all but Lubuntu is the best thing they have going for them. Really nice.
Debian Lxde is all right but it is straight up Lxde and pretty bare bones. Worked the last time I checked in when Wheezy was testing.
12.04 was based on Debian testing when Wheezy was Debian testing. As you were running it this may work.
One thing you may want to consider doing if you have another computer is burn this image to a disk and then installing it on a usb stick. I am not talking about putting the ISO on the stick. I mean formating the stick to ext4, making 2 partitions (/ and /home) and installing from the DVD. Then assuming the DVD will boot but won't install, you can boot to the DVD insert the stick in a usb port, and the dd command to copy the Stick to the hard drive
Another thing you could try if you want to stick with the Ubuntu family is to get the netinstall image. This is a text only installer and doesn't install much. It will give you a kernel, full file system and the APT system. It will boot to a tty login and you install the rest of the OS from there with apt-get.
The Ubuntu meta packages are quite a bit bigger than most distros use and this makes a netinstall some what easier. The meta package for most DEs includes all the xserver stuff you need to have graphics for the gui instead of just the DE packages. So one command should get you a working system.
If Ubuntu or any of the family members are still putting out an alt-install disk that would probably work for you too. It uses the Debian default installer with no live session.
Seeing how you had 12.04 running I think your problem is the Live Session is just too damned big for your meager ram. The alt-install disk would not be that heavy. Shouldn't be a lot heavier on your system than the netinstall image really (same installer).
Unlike the netinstall image it will install the entire OS. Also includes a menu option of booting to rescue mode to rescue a broken system. Will basically set up an chroot for you so you can deal with the broken system and fix it.