Check to see how many things are loading during boot up. If there are items that can be disabled because they are not essential, go ahead and "disable" them to speed up booting up.
How often is the machine cleaned? Something like
CCleaner, is a
freeware system optimization, privacy and cleaning tool. There is a
Slim version available as well at
http://www.piriform.com/ccleaner/builds - 4th option down. It removes unused files (cache, temporary Internet files, etc.) from your system - allowing Windows to run faster and freeing up valuable hard disk space. It also cleans traces of your online activities such as your Internet history. Additionally it contains a fully featured registry cleaner; I recommend making a back up in My Documents prior to doing a registry cleaner as a "just in case."
How often is the machine defragged? There are many tools out there, but one that is
free and easy to use is by
Puran http://www.puransoftware.com/.
These items listed above will not speed up how quickly the Avast shields load, but they will speed up the machine. However checking on what is loading on boot up may actually help speed Avast loading depending on what and how many things are competing at the same time.