Macbook Pro Ram and/or Processor broken?
While hard drives are the most likely component to die in any computer, memory can and does fail from time to time. An "Early-2011" model will be nearly four years old now so it's worth considering an HDD replacement at some point (these were some of the first systems to feature SATA-III controllers so you will be able to take full advantage of current SSD speeds).

However, if AHT is detecting memory issues then that's the area to focus on. Booting from USB is obviously independent of any potential hard disk issues and boot failures are nearly always guaranteed to be down to memory issues.