Random BSOD that occur 0x000000be/attempt to write on read only memory

My computer has recently started having this random BSOD, after working normally for the last few years. The first BSOD had happened on 9/12/15 while playing the game Subnautica; after this blue screen, the computer rebooted only to get the same BSOD again. I then did a system restore to a previous point and the blue screens stopped, though they returned today (9/19/15) again. This time the BSOD happened randomly as soon as windows was started and loaded up the desktop.
What I have noticed is that prior to these BSOD, there has been a quite high usage of RAM (and wuauserv was also using lots of computer resources), even when here were no programs or games running. I'm not sure what caused these blue screens since there were no dmp files made during the previous BSOD, only on the most recent one.
I also noticed that in the BSOD, it said something like "Attempted to write in read only memory"
Today after the computer rebooted from the BSOD, I got this displayed:
"Problem signature:
Problem Event Name: BlueScreen
OS Version: 6.1.7601.2.1.0.768.3
Locale ID: 1033

Additional information about the problem:
BCCode: be
BCP1: FFFFF900C2B82000
BCP2: 55900000BD583021
BCP3: FFFFF88009BF7BA0
BCP4: 000000000000000B
OS Version: 6_1_7601
Service Pack: 1_0
Product: 768_1"
and this in the event viewer:
"Log Name: System
Source: Microsoft-Windows-WER-SystemErrorReporting
Date: 9/19/2015 1:11:31 PM
Event ID: 1001
Task Category: None
Level: Error
Keywords: Classic
User: N/A
Computer: Alienwarex51-PC
Description:
The computer has rebooted from a bugcheck. The bugcheck was: 0x000000be (0xfffff900c2b82000, 0x55900000bd583021, 0xfffff88009bf7ba0, 0x000000000000000b). A dump was saved in: C:\Windows\MEMORY.DMP. Report Id: 091915-17643-01.
Event Xml:
<Event xmlns="http://schemas.microsoft.com/win/2004/08/events/event">
<System>
<Provider Name="Microsoft-Windows-WER-SystemErrorReporting" Guid="{ABCE23E7-DE45-4366-8631-84FA6C525952}" EventSourceName="BugCheck" />
<EventID Qualifiers="16384">1001</EventID>
<Version>0</Version>
<Level>2</Level>
<Task>0</Task>
<Opcode>0</Opcode>
<Keywords>0x80000000000000</Keywords>
<TimeCreated
</System>
<EventData>
<Data Name="param1">0x000000be (0xfffff900c2b82000, 0x55900000bd583021, 0xfffff88009bf7ba0, 0x000000000000000b)</Data>
<Data Name="param2">C:\Windows\MEMORY.DMP</Data>
<Data Name="param3">091915-17643-01</Data>
</EventData>
</Event>
"SystemTime="2015-09-19T17:11:31.000000000Z" />
<EventRecordID>180435</EventRecordID>
<Correlation />
<Execution ProcessID="0" ThreadID="0" />
<Channel>System</Channel>
<Computer>Alienwarex51-PC</Computer>
<Security />

Also after the BSOD that happened today, the computer wouldn't start up; It was just beeping continuously. I had to unplug it from the wall and replug it back for it to restart. Once again I did a system restore. Help would be appreciated for this BSOD.

Hiya and welcome to SevenForums!

Code:

BugCheck 4E, {8d, 113f80, 510001, fffff68000068bcb}

Probably caused by : memory_corruption ( nt!MmZeroPageThread+96c )

Code:

BugCheck BE, {fffff900c2b82000, 55900000bd583021, fffff88009bf7ba0, b}

Probably caused by : win32k.sys ( win32k!vFillGRectDIB32BGRA+2a9 )

Run sfc /scannow and chkdsk /r.
Install the latest updates from Windows Update.

Do the exact same steps for chkdsk /r but instead of typing in sfc /scannow type chkdsk /r.

Run MemTest86+, It must be MemTest86+. RAM - Test with Memtest86+

Update your USB drivers.