In addition to what Usasma said...
Memory dumps are produced only as a result of an instance of a class of crash known as a "bugcheck" (a BSOD). If the machine is suddenly powering off or mysteriously spontaneously rebooting
without a bugcheck, then not only will there be no memory dump, but the troubleshooting approach has to be completely different.
The events you've noted are side-effects of the fact that the machine had just powered down "ungracefully" - they are not causal. Once the problem is rectified, those events will go away.
In the majority of cases, that "sudden power down" symptom is caused by hardware issues: bad or inadequate power supply, borked motherboard, over-clocked processor being unable to cope... the list of possibilities is very broad.
Unfortunately, the event log is rarely useful in these cases because the sorts of root causes capable of completely powering down everything without much ceremony also tend to preclude the logging of events. In other words, there's none of this business: "oh, wait, I know you wanted to die miserably because the PSU +12V rail just dropped to 2V, but I'd really like to spend a second or so first logging an event to say how sorry I am that this is about to occur."
Suggestions:
- Try running hardware diagnostics, especially if the hardware is relatively new and untested. Memory diags and CHKDSK /R in particular.
- Make sure you're on the latest BIOS for that motherboard.
- Update all the NIC, chipset, video... drivers.
- Don't overclock
- Open up the side of the case and test whether pointing a large mains fan on "full blast" squarely at the motherboard makes a difference to the frequency of the power-down symptom, in which case it's related to (too much) heat.
- Boot to safe mode (press F8 at startup) and leave/use the machine there long enough to form an opinion as to whether the power-downs still occur.
- Test what happens if you leave the machine in the BIOS config menu for many hours - over the weekend if necessary. If it still produces the same symptom and powers itself off... something's badly broken and it has nothing to do with the software.