Maybe I'm totally out of date with this but...
You can reinstall windows w/o format, and have access to your old files in your new windows copy, install a burn disc program or connect to another pc and back up your files.
That is the cheapest way, about the external case you need a 2.5in as typongtive said, but I'm wondering since that blue screen is only one of 2 posibilities, your RAM is failing or your HD is failing, what I mean is even if you back up and format again it doesn't warrant that you lap will work fine after that.
What HP support center asked you to do was a BIOS reset(hold power button for 30 secs) mostly that work if you lap got an electric shock, and the system block itself to prevent further damage, but no way to help with a blue screen with that.
Hope it helps, let me know if I can help you with something else.
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"Maybe it means: you're the evil man, and I'm the righteous man, and Mr. Nine-millimeter here, he's the shepherd protecting my righteous *** in the Valley of Darkness." - Jules.
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