Find out WHAT manufacturer made the hard disk. Download the diagnostic software from that manufacturer. The main hard drive makers are Western Digital, Seagate, and Toshiba.
It will look something like this;
As for linux, it doesn't NEED a hard disk to run, so try booting it from the DVD you created or purchased with the hard disk removed from the laptop. It is also extremely stable. My desktop I leave on all the time, just let it sleep between uses, it's a lower power unit, here's one time I did page capture just to show how stable it was, no reboot over 100 days, even after multiple updates to the system. Unlike windows, you only need to reboot for updates if you install a new kernel and want to boot into it. (the old kernel remains for use if needed or desired)
In fact, I don't even use a hard disk in my old laptop with Linux, I have it installed to a $10 flashdrive which I keep on my keychain. Added benefit is my data is encrypted, so if lost, no worry. Even better, windows computers can ONLY read the first partition on a flashdrive, so I sometimes install mine to a second partition I create on it using GParted, leaving the first as FAT32 to use for file sharing when wanted. If I do a full install, then using EXT* file systems is sufficient for denying windows users to the data, and "on the fly" encryption locks it up the rest of the way.
My use of both go back aways.
Here's a Kubuntu (12.04) I run from a 16 GB Kingston Flash Drive.
For you, I made this screen capture of a Mint 17 MATE flashdrive. You can see the Home folder for Mint 17, and it says Empty because that's what it shows when encrypted and viewed in a file manager by someone else. Unless someone has the password, all they can recover from it are encrypted files which are worthless to them. The flashdrive is 16GB in size, the fully installed system (different than using LIVE type install) is about 5GB of that, the rest is for data. Full install would normally be about 8GB in size, but for more data room I stripped out some programs I won't be using. I plug this into my laptop USB port and boot from it.
There's no reason a failed hard drive should should sideline your laptop. You can put an LIVE install on the flashdrive, or a FULL install.