El-capitan crashing while booting Objective:


Somehow I want to fix the issue and should be able to login to the El-Capitan without reformating as so many valuable files are there
Find what has caused this problem so that I can avoid this problem in future


Overview:

I have two drives on my mac desktop one is Macintosh HD and the other one is El-Capitan and El-Capitan is my start up disk.

It was working nicely for long time, then all of a sudden one day El-capitan started showing trouble logging into the account.

some applications disappeared from applications like chrome

I couldn't open any apps it always showing the color wheel

then all of a sudden whenever i try to boot up in the el-capitan system started crashing now I am unable to log in to the el-capitan drive.

But I am able to login to Macintosh HD which runs on Yosemite

The below pictures will depict all the ways I have tried to solve the problem but nothing fixed it.















References

https://support.apple.com/en-in/HT203176

https://support.apple.com/en-in/HT201262

Possible solutions:


They say DiskWarrior can fix this but that is not free
Take the backup of files and reformat the drive again which I don't want to do unless there is no other way 


Note:

I didn't any backup mechanism like using TimeMachine

I would like to leave no stone unturned

Thanks for any help in advance

Update:
Here is S.M.A.R.T status
I/O Error usually means your disk has hardware failure. I would backup everything ASAP and change the disk. Disk Warrior will probably not solve the issue as it's only repairing a corrupted filesystem.

If you can mount it at some point (try repeatedly), use Carbon Copy Cloner to backup your important data on a new drive. If you can't, try some recovery software like Data Rescue.