After login mac is stuck on progress bar I have 15 inc Mac book pro with Mavericks installed. I can successfully on the Mac but I cannot login to my account. Upon press enter I get progress bar and after that I get grey screen then nothing happened. 

I tried all those online solution i.e press cmd + s and follow:

/sbin/fsck -fy /
/sbin/mount -uw /
mkdir /Disabled_System_Library_Extensions
cd /Disabled_System_Library_Extensions
mv /System/Library/Extensions/ATI* .
mv /System/Library/Extensions/AMD* .
touch /System/Library/Extensions
exit

But I have no luck resolving this issue (this is the second mac that happened). I can sure see both Hard drive (HDD) and see all the context in by using cd, ls etc.. commands in this mode. 

I have also try changing the HDD that contain new OS (EL Capitan) but its the same old issue (also tried cmd+alt+p+r too). When I press Alt on startup I can see the HDD, so I guess the laptop can read HDD but cannot access it?   

One things I have also noticed is that I cannot start anything and what I mean by this is if I press cmd + R to access disk utility I persist same issue, if I try installing new OS via USB i  persist same issue. AND sometime when I login and keep the laptop for few long then my screen turns blue which forces me to restart my computer and follow the same procedure.  

It will be nice if someone can help, can access var/log via cmd + S, if anyone requires specific log let me know.
If you're able to boot to the installation drive (external USB, DVD, etc.) but not able to boot from an internal drive, that indicates a hardware problem, likely with the drive or the cable attached to it.

An easy test is to attach your internal hard drive externally with something like this. If it boots fine externally, you can be fairly certain that there's an issue with the cable (or, less likely, the Logic Board).

If you still have trouble when it's connected externally, then you should first try reinstalling the OS while it's connected externally (as you might still have some software corruption). If it persists after that point, you likely have a bad hard drive.