Symantec AntiVirus is Norton Antivirus. I am 1000% sorry. Had your log and another printed out sitting here side by side and picked up their McAfee listings and thought they were yours I am sorry.

Glad you removed the NOD32 though.

Now for your logs...
first of all you noted avgas.exe running in processes, that is the AVG Anti-spy program.
Running RegCure many times
this is NOT a good idea. For one thing cleaning the registry is good at times, but you also run the risk of cleaning out the wrong thing. Plus, this can make it much harder to actually find out what is causing a problem.

Can you give us more info on the computer itself...hard drive size, how much RAM do you have installed?

Also, please don't download anymore programs or do anymore cleaning until we can see if other steps are needed. By using other programs AFTER doing these scans the results are now skewed because some things showing in the scans may now be gone.
Can you do those steps again for me please and post the results.