Getting rid of Trojan-Dropper.Win32.Agent.aayv

My anti-virus software recently detected the Trojan-Dropper.Win32.Agent.aayv virus and quarantined it but stated it could not disinfect the system. I deleted it from my quarantine. How do I make sure that I was able to delete it and it's payload. My computer has been a bit slower and my internet goes down from time to time. The Anti-virus program I currently use is the Verizon Internet Security Suite. I have had other problems with it because it has been taking extra time when I shutdown my computer saying that it is trying to end UIPopupHidden. I am willing to put in the time to rid my computer of anything still on it that should not be there. I just need to be pointed in the right direction. Any guidance will be appreciated.

Thanks!