If it were me and I didn't want to rip the thing apart to start diagnosing at the hardware layer, I would start by:
- Verify the BIOS is up to date. Newer windows updates can conflict with older BIOS. They should be kept up to date together.
- Disable any devices in the BIOS that are not actually used.
- If that doesn't help, disable any "AI" overclocking or other overclocking especially if the laptop does not have an unlocked CPU that officially supports overclocking.
- If that does not help then I would suspect either power supply going bad or something got into the vents of the laptop and is periodically shorting something. Compressed air or "canned air" can help. Remove the batteries AND then hold down the power button for 20 seconds. If you can and use compressed air to clean out the laptop. Keep the can upright and adjust the position of the laptop, not the can. Blowing dust bunnies out often is good to do regardless.
Some newer laptops maybe yours counts can start acting weird if they don't get a motherboard reset from time to time which requires holding the power button for 20 seconds to turn it on and holding it for 20 seconds to turn it off at least every once in a while. Sounds silly I know but the Lenovo's from that period are notorious for this and I would not be surprised if other vendors had the same issue. No idea what if any shared components exist between an Alienware and a Lenovo.