The important part is here:
mce: [Hardware Error]: Machine check: Processor context corrupt
Kernel panic - not syncing: Fatal machine check
A machine check is a signal directly from the CPU itself that a serious error has been detected. Unfortunately, the most common reasons for machine checks are various kinds of hardware faults. It might be:
- simple CPU overheating (clogged air vents? heat sink not properly attached to CPU?)
- RAM failure (run a memory tester overnight if possible)
- data corruption on system bus (usually requires motherboard replacement, which may or may not be cost-effective on a laptop = warranty replacement of the complete computer might be in order)
- something else (this list is not exhaustive)
Your first goal should be to get any irreplaceable data backed up somewhere outside the laptop. If you don't already have external backups, you might need to do something like removing the SATA HDD/SSD or the M.2 SSD module from the laptop, plugging it to an appropriate external enclosure and copying your data out of the drive that way. If you feel you're out of your depth here, get a professional involved.
The second goal is getting the hardware fault diagnosed and fixed. If the system has detachable RAM memory modules, and there is more than one of them, you might try running with just one module installed. Try each module at a time: if one works and the other fails, you'll know which one of the modules is bad. If there is just one memory module, you'll need to get a second compatible module for testing. If the memory modules are not user-replaceable in that laptop model, that kind of testing will obviously be impossible.
At this point, you will have done essentially everything a skilled amateur can be expected to do with a problem like this one.
Even if the system is still under warranty, the sad reality is that you'll probably first have to prove the problem also exists when using a supported OS, i.e. Windows. But that error looks severe and repeatable enough that it will probably also crash the Windows installer, so be sure to try that, so that you will be able to honestly say you tried. It will probably be proof enough to get the warranty replacement process started.