According to the original HJT log the computer really has lots of infections on it.

I would also like you to run SDFix
Download SDFix from the link above and save it to your desktop.
Now, double-click on the SDFix icon that should now be residing on your desktop. If a Open File - Security Warning box opens, click on the Run button.

A window will now open showing SDFix being extracted into the C:\SDFix folder. Once the installation program has finished extracting SDFix, it will open a Notepad with further instructions.

Next, please reboot your computer into Safe Mode by doing the following:

1. Restart your computer

2. After hearing your computer beep once during startup, but before the Windows icon appears, press F8.

3. Instead of Windows loading as normal, a menu should appear

4. Select the first option, to run Windows in Safe Mode.

5. When you are at the logon prompt, log in as the same user that you had performed the previous steps as.

When your computer has started in safe mode, and you see the desktop, close all open Windows.

Click on the Start button, click on the Run menu option, and type the following into the Open: field:

C:\SDFix\RunThis.bat

# Then press the OK button.

# The SDFix window will open containing some brief info and a disclaimer on the use of the tool. Please press the Y key on your keyboard and then press enter.

SDFix will now start scanning your computer for known infections.
This process can take a while, so you may want to do something else and periodically check back on the status of SDFix. As the scanning process continues you will continue to see new messages on the screen.

When the scanning process has finished you will see a new screen stating that you need to restart your computer in order to continue.

At this point you should press any key on your computer's keyboard in order to restart the computer.

After your computer reboots SDFix will automatically start and perform a last check.

You will now be presented with a screen stating that SDFix has finished.

At this point you should press any key on your computer's keyboard in order to continue to your desktop.

When you are back at your Windows desktop, the SDFix log will automatically be opened in notepad.
Please Save that log for posting here.

Reboot the computer.
Update MBA-M and run one more Full Scan with it. Allow it to Remove anything found.
Save the log.
Reboot the computer and run a new full system scan with HJT. Save the log.
Post back here with all requested logs.

Also I would like to see an Uninstall list done with HJT. To do that do the following:
To access the Uninstall Manager you would do the following:

  1. Start HijackThis
  2. Click on the Config button
  3. Click on the Misc Tools button
  4. Click on the Open Uninstall Manager button.

Click on the Save list... button and specify where you would like to save this file, the desktop is the easiest. When you press Save button a notepad will open with the contents of that file. Simply copy and paste the contents of that notepad
Judy