My ax3400-e4502 started running extremely slowly.

Sounds like possible malware or viruses, i personally would avoid backing anything up and wiping the drive with a fresh install of windows.

I am assuming your not getting any errors pop up such as dead ram or similar, if it was HD i would imagine there would be no prior warning i know mine went on my imac running windows 8.1 on bootcamp (but i dont recall how i came across the issue).

If your sure its NOT hardware i would go ahead and do a clean re install before any malware or virus kills your HD or worse, not 100% what the worst case is for those problems but i would avoid it before it becomes and issue.

And by pass the restore it wont resolve the issue if its malware or virus as its on your drive now (IF) that indeed is the problem.

P.S

I should also note that before taking such drastic measures maybe a clean out of your hard drive such as deletion of any unneeded softwares etc, then defrag that may also be an issue....