Where are you getting the information about the kernel errors? That's what I'm looking for as I specialize in them.
The STOP 0x7A (shorthand for the 0x0000007A number) indicates that the requested page of kernel data from the paging file could not be read into memory."
The paging file resides on your hard drive - and it uses the NTFS.sys driver to read from the file system on the hard drive.
More info on this error here: http://www.carrona.org/bsodindx.html#0x0000007A
The Usual Causes section of the link cites both the hard drive and memory as some of the possible causes.
So, start with these free, bootable diagnostics (particularly the memory and hard drive tests): http://www.carrona.org/initdiag.html
If that passes, then run "CHKDSK /R /F" (without the quotes) on ALL hard drives from an elevated (Run as administrator) Command Prompt. It'll say it can't do it now, and will offer to run it when you reboot. Accept that choice and reboot the system and let it run.
Just FYI - iIf the system is generating different errors when it crashes, that is most likely a hardware problem (some software issues also act as if they're hardware - especially lower level drivers). Consistent issues with the same error code usually denotes a software issue (with some exceptions there also)