Many popular Linux distros (e.g. Ubuntu) can be booted as a "live" distro which runs directly from the installation media and doesn't touch your hard drive unless you ask it to. Diagnostics which aren't included in the base image can be installed over the internet from the distro's repository even into a "live" installation; any software installed while running in "live" mode gets transparently installed to a ramdisk and therefore is implicitly uninstalled the next time the system is rebooted.
There are also distros which are designed from the ground up to be used as a "live" distro, without installation to the system drive, e.g.
Knoppix.
If you're completely unfamiliar with Linux, a better approach might be one of the bootable system diagnostic images, like
Ultimate Boot CD (in spite of its name, you can also boot it from a thumbdrive, so a CD/DVD drive is not required).
While it is entirely possible that the drive is toast, it is also possible that the disk is just partitioned in a way which is badly confusing Windows. If this is the case, simply wiping the existing partition table (or doing a "write zeros" to the drive) so that it appears to be "factory fresh" may restore it to usefulness. You should be able to do this with the Ultimate Boot CD image.