Do you see the image I posted, when you press the Ctrl+Alt+Delete together ?
Nothing is in order until you click the column heading to order it.
The PID, I thought I explained is the Process Identity number (as indicated in the arrowed column in the image), each process in the task manager list has a unique process identity number. We are looking for the "FILE NAME: Process386," mentioned in the pop-up information you gave, I'm hoping that it might be the PID I'm talking about and reveal something that may help us track down what it is.
It may be that avast blocked it when it was loaded into memory, but we are trying to find what tried to load it, that remains undetected. It is never at square 1 you have tried something that didn't work, we move on to the next step.
If you haven't already got this software (freeware), download, install, update and run it, preferably in safe mode (
http://www.pchell.com/support/safemode.shtml).
1. If using winXP
AVG anti-spyware (formerly Ewido). Or
SUPERantispyware Or
Spyware Terminator.
Try downloading these one at a time (the blue text is a link) and running them to see if they find anything, what ever is found make notes and don't delete anything quarantine is the safest option. Try not to see it as a huge task, but see it as a series of steps, take one step, report your findings and if need be take the next step.