Trojan Removal

Hello, everyone. I'm having a problem with a Trojan and would greatly appreciate anyone who could help resolve this issue.

My computer was hacked by a RAT (Remote Access Trojan), so I did a system restore and then restored my computer to factory settings. However, I'm not sure that it's truly gone.

I'm not so sure it's gone because sometimes odd things will happen, such as a command prompt will pop up for a few seconds and then disappear in a flash. It never used to do that before. Another reason why I'm not so sure that it's gone is because I can still recover things from before I restored to factory settings. I downloaded Recuva, a program that is designed to recover deleted information. I just ran it to see what it would bring up and it brought up all my documents that were deleted when I restored to factory settings. I didn't download the things Recuva brought up, but it worries me that all my old documents are still hidden on my computer somewhere...because that means the RAT could be hidden there also. Can a Trojan still be active even after a factory restore?

How can I make sure it's truly gone? And I don't have a windows installation CD.

I've tried scanning my computer with my antivirus programs and looking to see if it's still here myself, but I'm concerned that it could be a "FUD RAT", where FUD stands for "Fully Undetectable". If it is that kind of Trojan, then I have no idea how to find out whether it's still here or not. And my antivirus programs could be missing it. When I look in the "processes" tab of the task manager, there's nothing suspicious there. But if it's a FUD rat then it could just be invisible.

Thanks in advance to anyone who tries to help.