Two important questions to answer:
1. Can this laptop boot from a USB drive, or only from an internal drive? IF it can boot from an external OPTICAL drive the next item can work. You'd still have to use BIOS Setup to tell it to boot from that external device. Even better: assuming the laptop has its own internal optical drive, forget the USB external. Just burn the CD on another computer, then put it into the laptop's optical drive and set it to boot from there.
2. What company made the malfunctioning internal HDD? Some of them have free diagnostic utility packages you can download from their website. But most of these ONLY work on a HDD made by that company. So, the the bad HDD is from Seagate, get their Seatools package. If it's from WD, get their Data Lifeguard package.
In each case, I much prefer to get and use the "for DOS" versions. With these you download an .iso image file. Then you have to use some utility software like Nero to "burn" this image to a CD. This creates a bootable optical disk. When you boot from it, it loads a mini-DOS into RAM and then runs a menu of tests and repair tools you can use. The beauty of this system is that it works even when the HDD in your machine does not - all it needs is to boot from the CD you burned.
A couple of important notes when you do this. First is to make SURE you are working on the HDD you want to. That's because the more advanced tools can destroy data, and you don't want to do that to the wrong HDD by mistake. The second is to note that the first tools you use do NOT destroy any data. BUT there are also advanced repair tools that DO destroy data. Generally these latter ones will warn you of the impending data damage and ask you to confirm your intent to proceed, so watch for messages before hitting "OK"!