Either you have defective RAM or a overheating CPU.
I think you may have a heat problem. My Compaq Evo N610c used to behave the same. The problem was that the Linux distros back then (2002 / 2003) when this laptop was sold did not yet fully support the ACPI BIOS that this stupid machine had. The consequence was that the internal CPU ventilator never activated and the machine overheated, causing the CPU to shutdown. Result: instant freeze or a very very surprising instant poweroff while I was sitting in front of the laptop ...
Can we try this? When you boot your Linux, hit F6 "Other Options" and then add these arguments to the kernel command line (before you boot your machine!):
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acpi=off apm=on no-hlt