Windows 7 updates fail to install

Please fill in your system specs completely, including all security programs you are using. This will help our experts when they drop by.

This tutorial by Brink will help you.

System Info - See Your System Specs

The error showing in your graphic is typical of a connection problem - often caused by firewalls.
What security software is currently installed?
What other AV's have EVER been installed?

No Anti virus ????

Is there ANY reason why you're not running an AV?
You are probably infected already - and possibly heavily so.

I'm going to ask for a malware specialist to drop by and advise.

Review Jacee’s instructions to run Adwcleaner here post #7,
Ignore the title of the thread,
https://www.sevenforums.com/system-security/316404-instant-savings-app.html
Screen shot of the download button to use for Adwcleaner
You can use these free tools to see if they find anything,
Manually Update them before running full scans,
Try not to use your computer while the scans are running, (one at a time of course).
See this tutorial on how to download and run Malwarebytes,
https://www.sevenforums.com/tutorials/338716-malwarebytes-anti-malware-free.html
Also use the Custom scan option not the Threat scan,

Please Do Not clean/ Delete or Remove Any detections before posting the scan results first before review especially Malwarebytes,
http://www.malwarebytes.org/products/malwarebytes_free
SAS is safe to remove anything it finds
http://www.superantispyware.com/?tag=SUPERANTISPYWARE
This one is the longest up to 4 hours, the others are only about 45 minutes,
http://www.microsoft.com/security/scanner/en-us/default.aspx

Post all scan results for review,
Cheers.

I had this update problem recently with a brand new laptop worked it out to be it did not have SP1 on it installed it myself and bingo in flooded the updates so check your system in Control panel and see what you have got form what I have quickly read through not much about the system per se'

For malware scan I would be inclined to start with this Download Kaspersky Rescue Disk 10 first before going any further and here are tons of on call scanners available.