Go into the bios,
usually on the first screen, or first option your see your disk and then 1.44" Floppy look for that select it and select disable, off, no floppy something along those lines
But honestly.
Ubuntu 7.04 doesn't look for the floppy, a floppy error wouldn't crash your system
K easy thing to check
Synronise your clock to the computer, wait for it to crash
Reboot
then check dmesg
dmesg|grep HH:MM
so if it died at 4:35:45
dmesg|grep 4:35
I'd also look at 4:34 and 4:36
you can also check for error but this can be a little more tricky
dmesg|grep -i error
dmesg|grep -i fail
put the out put of these commands, if you can figured it out from reading them, at the end of this post.
Sound like a hardware problem, but dmesg could point you in the direction of the problem for you to fix it.
My best guess with this little bit of information(especially since you say it crashes on memory test)
MEMORY or MOTHERBOARD, less likely processor.
Also I see you have ssd, make sure you have no_atime or noatime in your fstab
But again, ssd shouldn't crash your system on idle, when you go to load a new program not in memory, possibly could cause it to freeze. But just leave the system idle and wait for it to crash. Possibly while at a console, cause a serious error will be spit to console.
(TO SEE The actual console hold ctrl+alt+f1[f1-f6 are usually your getty ports, and f7 is usually reserved for X but I've also seen f6 and f8 and you can of course change this yourself])