Windows Updates Error Code's 8024000E & C80003FA

Aha!

wuaueng.dll (128) SUS20ClientDataStore: The database page read from the file "C:\Windows\SoftwareDistribution\DataStore\DataStore.edb" at offset 98304 (0x0000000000018000) (database page 2 (0x2)) for 32768 (0x00008000) bytes failed verification. Bit 131873 was corrupted and has been corrected. This problem is likely due to faulty hardware and may continue. Transient failures such as these can be a precursor to a catastrophic failure in the storage subsystem containing this file. Please

wuaueng.dll (128) SUS20ClientDataStore: The database page read from the file "C:\Windows\SoftwareDistribution\DataStore\DataStore.edb" at offset 98304 (0x0000000000018000) (database page 2 (0x2)) for 32768 (0x00008000) bytes failed verification. Bit 801 was corrupted and has been corrected. This problem is likely due to faulty hardware and may continue. Transient failures such as these can be a precursor to a catastrophic failure in the storage subsystem containing this file. Please contact your hardware vendor for further assistance diagnosing the problem.

You also have massive problems with the Bonjour Service (from Apple) - but that's so common I usually ignore it.
TombRaider is throwing a few Access Denied errors, and RealPlayer and Adobe Air are also throwing errors.

I think a CHKDSK is in order here...

Click on Start > All Programs > Accessories
Right-click on the Command Prompt entry
Select Run as Administrator and accept the UAC prompt - the Elevated Command Prompt window should pop up.
At the Command prompt, type
CHKDSK C: /R
and hit the Enter key.
You will be told that the drive is locked, and the CHKDSK will run at the next boot - hit the Y key, and then reboot.
The CHKDSK will take a few hours depending on the size of the drive, so be patient!
After the CHKDSK has run, Windows should boot normally (possibly after a second auto-reboot).

Please then rename the SoftwareDistribution folder -

Open an Elevated Command Prompt
Run the following commands

NET STOP WUAUSERV
REN C:\WINDOWS\SoftwareDistribution SDOLD
NET START WUAUSERV

reboot
then wait 10 minutes, and open Windows Updates, and run a Check for Updates.

Install only the oldest update found - and reboot once installed
then go back to Windows updates and install the others.

Please post the new C:\Windows\windowsupdate.log files - and new event logs.

(Both the above errors are indicative of problems with the connection between you and the Windows Update server.)

There are still a number of corruptions appearing in the current event logs - but the disk appears to be fine.
This means that the most likely source of the corruption is RAM
Please follow the RAM test tutorial here... RAM - Test with Memtest86+ - you need to run at least three full passes without any errors to be fairly sure that the RAM is OK. (some like to run 7 or 8, but I think that's probably excessive)

That leaves me a little confused
I saw a couple of BSOD's in the logs, so let's have a look at the data...
Blue Screen of Death (BSOD) Posting Instructions
post the generated files here rather than elsewhere - I'll get one of the specialists to pop by and give it a once-over.

The crash dumps are 9 months old, at least. So those will not reflect the present situation at all. But .... there are some things those you need to do.

Daemon Tools, Alcohol 120% and Power Archiver Pro uses SCSI Pass Through Direct (SPTD), which is a well known BSOD causer. Uninstall Daemon Tools at first. Then download SPTD standalone installer from Disk-Tools.com, and execute the downloaded file as guided below :

• Double click to open it.
• Click this button only:
• 
• If it is grayed out, as in the picture, there is no more SPTD in your system, and you just close the window.

Free up the startup. Windows does not need any other program to auto start with it, but the auto start programs often conflicts and causes various problems including BSODs.

1. Click on the Start button
2. Type “msconfig (without quotes), click the resulting link. It will open the System Configuration window.
3. Select the “Startup” tab.
4. Deselect all items other than the antivirus.
5. Apply > OK
6. Accept then restart.

You have some factory bloatware installed, too. Uninstall them.

Start Menu\Programs\ASUS
Start Menu\Programs\ASUS\AsusUpdate
Start Menu\Programs\ASUS\EPU-4 Engine

And, as the computer is substantially old, is the computer hot? Report us the heat of the computer after a couple of hours of your normal usage. Upload a screenshot of the summery tab of Speccy. Alternatively, you can publish a Speccy snapshot too: Speccy - Publish Snapshot of your System Specs .

Check if the Power Supply Unit (PSU) supplying adequate power to the computer or not.

• eXtreme Power Supply Calculator - The only power supply calculator trusted by PSU manufacturers and computer enthusiasts

Also let us know the wattage of the installed PSU.