What do I do when extensive SWAP access makes system dead

You're experiencing thrashing due to exhaustion of physical memory, so the system is constantly swapping memory pages in and out of disk.

http://en.wikipedia.org/wiki/Thrashing_%28computer_science%29

Three possible solutions:

1. Buy more RAM
2. Try a different browser to see if it has a lower memory usage until you can get more RAM.
3. Don't open so many facebook tabs until you buy more RAM.

As to how to do a proper shutdown, you can try the REISUB sequence (http://kember.net/articles/reisub-the-gentle-linux-restart/). Failing that, you'll probably just have to risk power-cycling the system.