REPEATED AND STILL UNFIXED SYSTEM ERROR DETECTED

I suggest you test your RAM using Memtest86 from GRUB as a good start point

There are No Errors with RAM it is the Maximum 2GB this motherboard can handle. In the Real World we are NOT made of money.

These Ubuntu ‘Critical System Error Detected’ errors, appear to be centered around something that was changed BY UPGRADES in the Ubuntu kernel, resulting in a Failure to clear ‘Old’ used ‘Inode’ strings, (such as when closing a browser Tab, etcetera).

..As when viewing YouTube videos, Or more specifically, when Google/YouTube messes up on correctly loading a subsequent ‘inode’ data section in playing back a video.

Or when the Facebook ‘Notification System’ - ‘Interrupts’ while viewing the News Feed page, or attempting to check on a notification by (Right Click Menu) in a new Browser Tab. Typically Crashing that Tab when Certain types of (Malware Encoded) Ads are attempted to be loaded in the Right Hand side, Page Column).

..This failure to clear ‘Old Inodes’ being made pronouncedly worse during the past few weeks, as Google/Youtube has been Reformatting its main landing page, as well as by Facebook attempting a still ongoing amalgamating of its ‘Notification System’ with its two newest acquisitions. - These ‘Critical System Error Detected’ errors, Still have Not been addressed nor remedied at this time.

As for the ability to run FSCK – FROM RECOVERY MODE – (Hold down SHIFT while booting): Ubuntu IS NOT YET LOADED at this time in the RECOVERY MODE, as this is a still a selectable option (as to which Ubuntu Variant is to be selected to be loaded) from the recovery mode Menu at this point. Which had worked fine up through Ubuntu 12.04LTS – 14.04LTS. But then in later releases was altered, so that although the FSCK option still appeared on the RECOVERY MODE menu, it was No Longer Functional.

As is: The 'Orphaned Inodes' appear in the Log presented on screen upon Forced System Restart/Reboot.. Requiring TWO full Restart/Reboot cycles to Clear them. Timing wise, it was previously faster to use Recovery Mode to clear them.

The amount of RAM is moot. It's the health of the RAM that is important

Frequent file system inconsistencies (e.g. 'orphaned inodes') can be an indication of hardware failures.
Have you verified that all cables to your hard disk(s) are firmly plugged into their sockets?

fsck is a program on the Ubuntu file system. How do you expect to be able to load the file system check program from the hard disk without mounting it?
The only reasonable way to run a full file system check on a file system is running it when the file system is not in use and is not mounted.
But discussing how to run fsck is only talking about the symptoms. The root cause for your frequent crashes must be something different. And the more often you write about these problem, the more I suspect that there is a hardware fault.