Fishrrman's rule #1 of Mac:
Never, NEVER, NEVER "wipe" a Mac's internal drive UNLESS you have a SECOND bootable drive (i.e., bootable "to the finder") by which to start it close-at-hand. And, TEST the backup first to know that it will work before you do the wipin'!
Having said that, I agree with the advice of others here to take the MacBook to a brick-n-mortar Apple Store RIGHT AWAY (provided one is close to you) -- they have a free repair program for the drive ribbon cable.
That might get the drive going again. A defective cable will make it appear as if the drive is dead (even when it's still fine).
BUT -- if you want to REALLY improve the laptop, put an SSD into it. A modestly-sized SSD is cheap (I would suggest either 240 or 480gb).
They are VERY easy to install -- a 15 minute job. ANYONE can do it.
Go to ifixit.com to see the procedure.
Be sure to use the right tools (phillips #00 driver and TORX T-6 driver, both can be found at hardware stores, Home Depot, Lowe's, and online).
I also advise folks to buy an external USB3 2.5" enclosure. Use this to "prep and test" the new SSD -before- you install it. Although in your case, if the hard drive has failed, this wouldn't matter.
If it's "just the cable", chances are the internal HDD is still ok. After you do the drive swap, put the HDD into the enclosure and use it for backup...