Blank screen after login (sometimes)

I cannot log in to Windows 7 Professional - all the system does is hang after initial login (after the password has been entered.) However, I can log in using Safe Mode with Networking (but not Safe Mode!). I did a chkdsk /f /r - it reported and repaired corrupt index entries. This let me log in normally but after a while, after a restart, same thing happened.
Disk is fine, Linux (I booted with a Live CD) reports that the file system is not clean.
I booted back into Safe Mode with Networking, ran sfc /scannow 3 times, said everything was working fine, no errors; ran Dism /Online /Cleanup-image /ScanHealth which yeilded the attached log file (RestoreHealth however doesn't work, presumably because the system I am working on is not Windows 8.)
I am running out of ideas!

See through this list:
- Boot with Last Known Good Configuration (F8 menu)
- Restore to a prior date (System Restore) - System Restore
- Scan for malware (Malwarebytes Anti-Malware free)
- Try a clean startup Troubleshoot Application Conflicts by Performing a Clean Startup
- Check if explorer.exe is running and start from CTRL+ALT+DEL (task manager - new task)
- Verify in registry: HKEY_Local_Machine\Software\Microsot\Windows NT\Current Version\Winlogon to make sure 'shell = explorer.exe'
- Follow SFC /SCANNOW Command - System File Checker
- Check Disk - Disk Check
- Try loading defaults in BIOS
- Update all your drivers
- Check out the interesting solutions in black screen with cursor only [Solved] - Cursor - Windows 7

GokAy said:

See through this list:
- Boot with Last Known Good Configuration (F8 menu) - The option isn't there. All I get is Safe Mode, Safe Mode with Networking, Safe Mode with Command Prompt, and Start Windows Normally.

- Restore to a prior date (System Restore) - System Restore - I did this, but System Restore completed unsuccessfully

- Scan for malware (Malwarebytes Anti-Malware free) - all clean

- Try a clean startup Troubleshoot Application Conflicts by Performing a Clean Startup

- Check if explorer.exe is running and start from CTRL+ALT+DEL (task manager - new task) - did that.

- Verify in registry: HKEY_Local_Machine\Software\Microsot\Windows NT\Current Version\Winlogon to make sure 'shell = explorer.exe' - affirmative

- Follow SFC /SCANNOW Command - System File Checker

- Check Disk - Disk Check

- Try loading defaults in BIOS - the machine won't let me load the BIOS!

- Update all your drivers - All up to date

- Check out the interesting solutions in black screen with cursor only [Solved] - Cursor - Windows 7

- will do this tomorrow.

Additions:

There are the odd occasions when I can boot normally but not that often.
I ran the Lenovo diagnostics - black screen occured while doing memory test twice. However, I did the Windows Memory Diagnostics and there were no errors detected. I tried to test doing Memtest, but the laptop kept rebooting, it wouldnt even start Memtest!

Memtest or Memtest86+? Should be 86+
RAM - Test with Memtest86+

It is indeed different that you don't get black screen always.

How does it not let you access BIOS? Error/nothing happens/no keys to press shown/etc?

This is very strange.
Won't let me run MemTest (CD or USB) or anything else - just automatically goes to Startup Repair!
F1 to get into the BIOS does the same thing so does F12 to boot from a temporary external device.

Are you sure keyboard is working properly? Do you get any feedback on screen upon F1 or F12? Is this a laptop or desktop?

Laptop and yes the keyboard is working properly, as I can press Enter to get into Startup Repair

Oh, just noticed you said "blank" not "black"
Tried a clean startup? Troubleshoot Application Conflicts by Performing a Clean Startup
What security software are you running?

I will ask others about the BIOS and Boot Menu.