I'm thinking of two possibilities. One is if your computer is set to boot upon power being applied (normally plugging a computer in won't boot it), and the power is blinking. You'd probably have to add an UPS with brownout protection to see if the issue stops before you'd know if it is a power line issue.
Power blinking might result in corruption while a system is running. If your computer suddenly just turns off it could be a "triple exception" where the CPU finds things so corrupt it simply shuts off to protect from further failures. If it shuts down in a normal sequence, then something else in software is causing it to shut down.
Try adding an UPS with brownout protection (the UPS does not have to have a long protection time...if it can run your system for even 3 minutes you will know a power blink can't cause your issues).
If the system shuts down normally, and if you have ruled out power delivery issues, then it is possible you have "wake on lan" (WOL) set up and your network card is receiving the magic cookie to power up or power down. I haven't used this, but perhaps there is a BIOS option related to WOL you can check for. Windows itself might also have some way of seeing what your WOL settings are...this would depend on the specific network card you have, e.g., integrated NICs may be more likely to have a setting in BIOS. Many add-on NICs support this feature.