Slow start up / boot of Windows 8.1, ASUS Vivobook S550CB

SSD missing from Disk Management. Faulty?

Hey guys,
I am very frustrated I really hope you can help me.

I have an ASUS Vivobook S550CB (Intel Core i7-3537u processor, 8Gb of Ram, 750Gb + 24Gb SSD hard drive) Windows 8 pre-installed. It used to boot/load Windows 8 and be ready to use it in 9-10 seconds. I updated to Windows 8.1 from Windows Store and everything was still perfect for the following 12-13 months.

Pushed the button, 2-3 secs ASUS logo, 2-3 secs Windows Logo and on the remaining seconds was loading the operating system
Now all of a sudden, after getting a message about a hard disk error/failure :
Push the button, 2-3 secs ASUS logo and then I see the "loading circle" under the logo "loading" for 4-5 minutes!! and after that loads the operating system just fine.

I checked the hard disks ( C: for the operating system, D: for the rest of my stuff, it was bought like this, with 2 partitions) with two ways:
1) Right Click -> Properties -> Tools -> Error Checking. Then "optimize and defragment "
2) I used the program Hard Disk Sentinel
Both ways showed no problem

So, having no clue about what happened I decided to reset my PC. I did that so I got the PC just like when I bought it... But with the problem still there! Updated again to Windows 8.1 and still there....

So now after all of this trouble I don't know how to fix the problem.

Any ideas?

(Btw I am not a PC expert so if you have the patience please be a little detailed on your suggestions if it's something complicated)

You mention, "hard disk/failure," but does that mean you've actually had a warning of a failure with the hard disk? I'm asking because if that's the case, then it's pretty obvious what's probably happened: you'll have probably had a hard disk failure. In this unfortunately event, backup your files and take the laptop back to the shop from whence it came, so they can replace the HDD free of charge. (assuming it's within the ream of possibility) If this is a no-go, you'll have to brave it yourself, or get someone else to do it.

But...

In the event that you can't do all that, and it is the HDD, then it's maybe possible to "workaround" this issue (not recommended due to possible, nigh-on-likely data loss) by flagging the bad sectors on the disk, but Scandisk should have done that really, unless you didn't do a thorough check; the one that takes an eternity.

Check the S.M.A.R.T status too, which you can do by downloading and running this tool: HDD Health failure prediction for hard drives and ssd drives (scan before running)

Good luck.

Thank you for your answer..

My warranty has expired and the store that I bought it from is a 9-hour drive journey so taking it to the store is not an option.

I've already backed up all of my files that's not a problem. The problem is that I can't afford a new HDD

I did a full disk scan using the CHKDSK command, everything was ok.
I've also used the HDD Health program you suggested, not a single problem as well.

Any ideas/suggestions?

I thing I found something that's not right..
On Disk Management I can not see the 24Gb SSD! Can't see it on Bios either, it says it's empty. So does that mean that the SSD is the one who's faulty? And if that's correct how does the operating system work? Is it loading from the recovery partition or something from the other hard drive??
(I am sorry for the questions but I don't know much about these)