Have you previously uninstalled Avira antivirus, that you used to use with Avast?
Does MBAM run resident, or is it the demand (free) scanner version?
If it is the free version, basically your system is not protected at all. Any number of malware infections could prevent an antivirus installing.
What is your operating system (including service pack number) and do you use any other security software? What firewall (if any) is operating?
What antivirus applications have been installed on this system in the past? (Avast included, if it has been.)