Here's what I will suggest on your Moms computer. As I write this, I will probably forget something, but its a start.
You will need AV protection. Recommended is Avira or Avast. I dumped AVG when it went to version 8.5 because of it being heavy on resources.
You will need a firewall. I only use windows firewall at present. I am considering zone alarm again. It is also very good. I tried comodo and found it difficult to use and configure, but that is probably me.
I would also suggest adding more ram. You can go to Crucial
or 4 All Memory
for an automatic scanner of the system. You can also put in your own specs to get what you need. You do not have to buy from them.
You should also clean off the old renmants of the old AV programs. Almost all of the AV providers have uninstallers. There is a link in my signature.
Continue to use MBAM. That is a good program.
Also, I suggest using Spyware Blaster
for preventing spyware.
As for the programs that run in the background, you should look at the msconfig (startup programs). Go to start.....run....type in msconfig. Go to the startup tap. All you need to do is uncheck the ones you do not want to start up when the computer starts. They do not get uninstalled by doing this, so you can go back in a recheck if needed. The ones to have automatically start are your firewall and AV/ malware programs. You just have to look at them and decide.
I will add that Erunt is a good preventitive choice to use.
Make sure that the windows updates are up to date also.
Please let us know if there is anything else we can help you with.