Why Didn't Norton Protect Me

Hello,

I am new to the Community but not new to Norton. I have used Norton for over 14 years and for the first time I am so disappointed with Norton. I usually use the Norton 360 but my husband wanted the Norton Security with Backup so we could put it on our tablets & cell phones. It's also on our PC. Couple days ago a friend took it upon herself to get on my computer & long story short, I had viruses & malware in my computer. When I came home I had a window saying to use Norton Eraser & from there this all happened: A Support Service named Bombar, Support logmeinRescue.com.exe & Instanttechsupport.com. All had remote control of my computer. They appeared one at a time. The last one, logmeinrescue.com tried to get me to pay 299.00 to get all the bad things they said were in my computer out. They all started a chat session with me. This all happened in a matter of minutes they just passed me off to each other. As soon as I asked them are you related in any way to Norton they said they were a Supportive Company for Norton. I cussed & told them the did not have permission to be in my computer & to get out. My words were not as nice as I just said them now. I worked for over 13 hours getting things out of my computer & I know I still have bits & pieces in there because my computer is running sluggish. Why didn't Norton Security with Backup protect me? And what do I do & use now to get the rest out? I was stuck with something called Internet Search as my home page. I finally had to do a system recovery but my computer is still infected. PLEASE HELP!!