Appears your version of MBAM is not the one that includes an AntiVirus so it should not mind having Avast.
AV: Microsoft Security Essentials (Enabled - Up to date) {71A27EC9-3DA6-45FC-60A7-004F623C6189}
AV: Avast Antivirus (Disabled - Out of date) {EB19B86E-3998-C706-90EF-92B41EB091AF}
AS: Microsoft Security Essentials (Enabled - Up to date) {CAC39F2D-1B9C-4A72-5A17-3B3D19BB2B34}
AS: Windows Defender (Disabled - Out of date) {D68DDC3A-831F-4fae-9E44-DA132C1ACF46}
AS: Avast Antivirus (Disabled - Out of date) {5078598A-1FA2-C888-AA5F-A9C66537DB12}
You will need to uninstall Microsoft Security Essentials since Avast won't be happy with another antivirus. I would probably download the latest (offline) version of Avast:
https://www.avast.co...ST&locale=en-us
Save it then uninstall both your old Avast and Microsoft Security Essentials, reboot then right click on your downloaded Avast file and Run As Admin.
Decline any optional software and stick with the Basic (Free) version. Do not accept the free trial. Once it installs skip the quick scan and instead run the Boot-kit-scan tonight while you sleep.
Click on the Avast ball. Then click on Protection, then on Antivirus, then on Other Scans then on Boot-time Scan. Click on Install Special Definitions. Click on Run on Next PC Reboot.
Reboot and let it run a scan. It may take hours.
Once it finishes it should load windows. Mute your speakers so it doesn't wake you up when Windows boots.
When you reboot you will see the scan start. It will tell you where it saves its log. Usually it's C:\ProgramData\AVAST Software\Avast\report\aswBoot.txt but it might change so verify the location. This is a hidden location so you will need to tell Windows to let you see it:
http://www.howtogeek...-windows-vista/
Copy and paste the text from the log to a Reply when done.