Ok you had a number of errors
0x24 (Twice) - Probable Cause "Ntfs.sys" - Normally problems associated with the HDD and also Anti-Virus software since you have already done the first steps i would have suggested for this error, next try disabling your Anti-Virus Software and Firewall, use the Windows Firewall as a temporary measure.
Note: The MiniDumps Indicate some sort of error accessing data at a certain address the same on both.
0x1E - Probable Cause "win32k.sys" - Normally caused by Invalid Memory or access violations - probably caused by hardware, since you have tested the RAM check your CPU (L2 Cache) by running Prime95 (Link Below). This will detect a error in minutes if any (Run the "Small FFT's" test).
OS 32bit Version -
http://files.extremeoverclocking.com/file.php?f=103
OS 64bit Version -
http://files.extremeoverclocking.com/file.php?f=205
0xA - Probable Cause "win32k.sys" - Most common causes can be bad device drivers but also can be caused by Incompatible Hardware and Software.
0x50 - Probable Cause "ntkrpamp.exe" - Normally caused by Defective Memory (L2 Cache, RAM, Video RAM) or Incompatible Software including Anti-Virus software.
0x1A - Probable Cause "ntkrpamp.exe" - Very similar error to 0x50 - The Minidump indicates a process called "SBCSSvc.exe" which is associated with something called CounterSpy i think from a Google search.
Which i guess is your Anti-Spyware i would suggest removing this because other process names include sidebar.exe and logon.scr which me guessing would mean some software at start-up or drivers are causing the system to crash so try to remove all software i suggested and also try cleaning your third party drivers out and reinstalling them fresh (Latest ones if possible). You will find all your device drivers at your manufacturers website
Use this to clean your Drivers out -
http://downloads.guru3d.com/downloadget.php?id=745&file=7&evp=54e6f91e495111338e2171476965c5ed
Simply tick the box "multiple cleaning filters" and go down the list adding all your third party drivers manufacturers.