I Can't remove Backdoor.Trojan and FakerAlert from computer?

On my computer, I have Spybot S%26D and Avast! Antivirus. Both programs are constantly updated along side Windows Update. I also have Norton Spyware Scan on my Yahoo toolbar as well. Norton Spyware Scan keeps finding Backdoor.Trojan and FakerAlert on my computer. Both Spybot and Avast dont find anything at all. So my question is why is the Trojan and FakerAlert keep coming back to my computer and how is it possible I can remove them FOR GOOD? I'd also like to point out that, I've looked up of how to remove them and I haven't had a straight answer as how to do so.

I Can't remove Backdoor.Trojan and FakerAlert from computer?security

I will research that Trojan for you because I currently have no idea what it is. In a few Min's I will update my answer but it still might not be of help to you.

Sometimes worms or Trojans can implant viruses/Trojans on your PC so if you remove the virus/Trojan the worm/Trojan can add it back again. Also some viruses come Thur the shared folder from an other PC if you have it setup like that.

Edited--- Just realized you do not know the name of the Trojan it is just detecting a Trojan. Each Trojan is different so it will be very hard for me to help you. I suggest you go to the store and buy the latest version of Norton anti virus because its much better then what you got. It will run you about $80 but even if it does not fix your problem it is still worth it because it will help you with lots of stuff.