1) What distro are you using?
2) What is the MODEL of your HP printer
When you get the Purple Screen can you Ctrl+Alt+F1 to get to the Terminal Screen , and try to update from there?
One thought is that you might have a video driver installed. Sometimes when you upgrade to a new kernel you have to re-install the video driver.
It's a bit long winded, but it's worth looking at. Perhaps you should start from the Partition that works and "Solution Two".
When you say it won't reboot, what happens, what do you see?
It may be my imagination but this problem seems to be happening a noticeable bit at the moment e.g. http://forums.debian.net/viewtopic.php?f=5&t=121269
If all else fails you may have to rescue your files and do a new, clean install. http://www.alandmoore.com/blog/2012/02/03/recovering-data-from-a-pc-a-guide-for-not-computer-people/#more-273
If you can download on Linux Mint 12, and you either know how to burn and ISO or USB stick, you should go for Linux Mint 17.1 Rebecca. It is supported until 2019.
What is the output of, if you put into a Terminal: lspci |grep Network
Your post suggests that you do not "know" Linux.
What do you mean by "laptop" driver? Linux is different from Microsoft Windows in that most "drivers" are already in the Kernel. They usually work out-of-the-box. It is not necessary to install separately.
The only additional "drivers" are commonly video and wifi.
Get a LiveCD and try it and see if it works. If it works, well..., it works and no addition is probably necessary.
It would be unwise to install Backtrack. Backtrack was replaced by Kali Linux.
If you are new to Linux, unless you have some special reason, it would not be wise to install Kali Linux.
According to the Kali website: "Kali is a Linux distribution specifically geared towards professional penetration testers and security specialists, and given its unique nature, it is NOT a recommended distribution if you’re unfamiliar with Linux or are looking for a general-purpose Linux desktop distribution for development, web design, gaming, etc."
If you use Ubuntu, when connected to the Internet open a Terminal and issue these commands:
sudo apt-get update
sudo apt-get upgrade
suso apt-get dist-upgrade
Mostly just a LiveCD...
If you have installed to the Hard Drive and the Boot Order/BIOS is set to boot from the Hard Drive first just leave it.
If you wish to boot from the CD-Rom and the Boot Order/BIOS is set to boot from the CD-Rom first just leave it.
Change it when it needs changing.