I tried googling around, and honestly, I can't tell how one is supposed to interpret the potential failing attributes that are provided. There seems to be no standard of interpretation available for the common individual, either. From what I could find though, it would seem those tests aren't always entirely accurate in detecting whether the HDD is failing. Due to the varied standards throughout the industry, these tests can only get you so far. I wouldn't take the test as the golden ticket that your HDD isn't failing, especially while exhibiting signs that it potentially is. It's now just a bit less likely that it's failing.
I would backup just in case. Better safe than sorry.
Something I should mention is that with my old computer, the HDD actually still does work. It found a second bout of life or something and stopped doing all of the errors that it was doing. We did nothing to try to solve whatever the problem may have been. It just sort of started reading correctly. The computer is rarely used these days though, so for all I know, it may only have a few more hours, a few days, a couple of weeks, maybe a few more months, potentially another year or two. Hard to say until the hard drive actually up and quits. Problems it had exhibited before we started getting the failure messages:
- Logged in, background was gone and replaced by some old looking blue one that I recall from old versions of Windows, theme was reset to the normal.
- Logged in, desktop was entirely unresponsive, despite mouse movement still being available. Ctrl+Alt+Delete was not working.
- Some error or another once a successful log in occurred at a random time. I can only remember that it required the computer being physically shut off via the power button.
- Failure to boot the OS.
- Failure to properly boot the OS, resulting in a mess at the log in screen.
- Finally being able to log in, only to be greeted by a message that the HDD is failing (words of my brother - I did not actually view this, but I guess the messages do occur if the setup is right for it.)
- The above happened over the course of about three days of trying to use the computer. A day later, the errors stopped, things started working again. Made a fresh backup to the 1TB external just in case.
Shortly after that, I moved, and my bro took the old computer with him when he split his way. I guess it still works, but as I said, it has received very little use the past six months. If I had to guess, it has maybe gotten about another 20 hours of use since July 2011, due to a lack of internet connection and no other use for it. For all I know, the HDD is ready to read its last bytes. Probably won't ever know, since I doubt that computer will still be hanging around for a whole lot longer.
tl;dr: It may be nothing that will resolve itself. It may be a HDD failure. I guess there is potential for a virus. Scan just in case, of course. If there's no virus, backup just in case. If you don't have a spare HDD, pick one up. Memory is inexpensive.