Boot scan is a special scan that is applied when Avast! tell you so. eg. You just finished a scan and Avast! found some malicious or suspicious file that might or might not be running and Avast! could not stop it. So Avast! wants to make sure, it did not miss it and asks for a boot scan. In this mode just some essential processes will be active in your computer and Avast! has a better chance to remove that malicous file.
If you really have problems with an infection, it is best to look for help here where a specialist can take a look at it.
http://forum.avast.com/index.php?board=4.0
No AV is really capable of completly cleaning a heavily infected machine. Remember that they are design to protect.