I don't think this model Acer has onboard diagnostics so in order to test the hard drive
you will need to create a boot disc that contains the test files.
Hard Drive Diagnostics Tools and Utilities (Storage) - TACKtech Corp.
Once you have this created you can test.
You can either look on the label or look in the BIOS for the make/model number
Since the Recovery Partition method does not appear to be working you would
need to order the Recovery Media from ACER or buy a retail version of Windows.