@Liz,
There might be other reasons for the problem, and the fact that Avast was running might be just a coincidence. We don't have enough info to be conclusive about it.
Are you using the battery only, or your system is connected to the power AC? Hardware is only 1 of many possibilities.
What I would suggest, so to confirm if Avast is currently related to the problem, is to completely unistall Avast. Do you have your registration file saved or backup-ed? If you do, then simply unistall Avast and shutdown completely your system (no standby nor hibernate, but power off).
If you can, leave the power cable connected but take out the battery (be aware of the consequences of this). Leave your system powered off until it cools down.
Now reboot; is your system working correctly? If it is, then Avast "may" be related. If it is still not working correctly, do whatever you need to do to make it work correctly. BTW, one reboot might not be enough to be sure it works or not.
In any case, if the problem is not consistent but only under some situation or "sometimes it works and sometimes it doesn't", then either some kind of update of some software is making problems, or a hardware problem is more likely.
To be clear, these are only possible suggestions. If you are not comfortable with hardware, or any of this seems "too strange" for you, then please don't start with any of these steps by yourself. Better to seek help from some friend or relative.
Whichever the case, please report back.