Windows 8 won't boot, I have a few ideas, need some

Things I have:
A laptop with a fully intact hard drive (Lenovo Y510P)
-No disk drive or external disk drive
-A version of windows 8 which is "missing some required information from the boot configuration data file" (error code: 0xc0000034)

A 1 TB USB external HDD (not 100% sure how much of this I can use, as it doesn't belong to me)
A USB flash drive with a few GB of data
Other working desktops with Windows 8 on them

So here are the options Lenovo gave me:
-Use the OneKey Recovery system from Lenovo to reset the computer to factory settings and have my computer working within 5 minutes, but also lose all of my data (not preferable)
-Pay Lenovo $120 to have them back up my files (not my programs) and then reset to factory settings (Also not preferable)

And here are some better do-it-yourself options I found from doing some research:
-Backup my data and re-install Windows 8 using the partition from another computer
-Backup my data and then do the OneKey Recovery thing and reinstall everything

So basically what I'm wondering is what I should do, and how I should do it without screwing things up.

Do you have access to another computer? If so, you may remove the hard drive and hook it up through an USB port and then copy all important data to a 3rd device of your choice. Then you can put it back to the original computer and do a full recovery w/o worrying about losing your data. Also, ALWAYS have at least 2 copies of any important data on separate devices because there's no fail safe hardwares.

Please contact a computer engineer/ computer expert.