me think of over heat condition which will cause many & varied snafu's.
How long since last cleaned professionally or even thoroughly at home?

Could be power supply over-heat shut down to prevent further damage?
Try removing both side covers & aiming fan inside. Does this extend time before shut down ?

Can't help you re: Linux story except if base conditions bad adding to it could only hurt?

Others may have better ideas which I welcome! Good Luck! Happy