What type of permanent damage could be done to my computer through remote access (TeamViewer)?

On some CRT monitors there was a relay that was engaged when changing screen mode. By changing screen mode repeatedly very fast, it was possible to destroy this relay.

Apparently some modern monitors can be wrecked by forcing them into invalid screen modes, but they must be pretty rubbish monitors.

Someone has mentioned flashing the BIOS to wreck that.

The microcode on some CPUs can be amended: wreck the CPU.

If it is a laptop, it may be possible to wreck the battery by reprogramming it: http://www.pcworld.com/article/236875/batteries_go_boom.html

With flash memory based SSDs or USB drives, re-write the same part of memory over and over to have it reach its end of life sooner.

On a cheap hard drive, forcing the stepper motor to push the drive heads fully one way beyond the end of the drive and then step back, repeatedly, could knock the heads out of alignment. I've known drives where the heads could get stuck if sent beyond their proper range (Tulip brand PCs in the 1990s).

I also wonder if you could change any BIOS settings such that the RAM or CPU or even GPU could be damaged, by overclocking or changing the board voltages.

Cook the GPU by driving it hard after over-riding its automatic temperature control. Ditto for the CPU.

Change BIOS settings to turn off the CPU fan then drive the CPU hard enough to cook it.

Let's assume the worst possible attacker. And for some reason, attacking without teamviewer isn't an option (like, the SMB bug, AMT in the CPU, any 0day from that angle, deliberate backdoors from MS and US government, ...).

Step 1: Using another 0day that only works if the attacker already has access to the desktop (but no admin) to get admin permissions. Then...

• Configuring Intels AMT (or AMDs counterpart). Result: Total control as long as a network connection is possible (even when the computer is turned off etc.).
• Flashing the BIOS/UEFI with something worse (because that usually needs a reboot, configuring Teamviewer to start at boot is helpful). Eg. to prevent that AMT is turned off again.
• Writing something to the hard disks spare sector area (that's not part of formatting) and/or flashing the hard disks firmware. To prevent you just switching the mainboard.
• Replacing some other firmwares, just to be sure.

...

And without 0days to get admin permissions? Or if the attacker just wants an more easy way? Well ... downloading child p*rn and then suing you. (And while sad, in some countries an IP is enough to go to jail. Even if you have evidence that you weren't at home where your DSL cable is, or anything like that.).
_{(Because the focus is on the computer: While you're in jail, the attacker enters your home and does whatever he wants with direct access to the hardware).}

They could pull a CIA and flash your HDD firmware, replacing it with their own infected version.

(Not sure you can do this to a VM though)