My two penneth.
Since you have an external backup, put Mint 17 on the laptop.
You can test it from a usb stick first to make sure it works - the wifi may cause a problem but the rest probably won't.
Then, when you've installed Mint, you can selectively replace any files you need from the backup.
Mint, or any other Linux distribution, has programs to replace the likes of Word, Excel, IE etc.
The thing will be faster than it ever was.