Trojan Virus - Is Computer Cleaned After Virus Infection?

I had a trojan Virus in the computer. I think that I got rid of it, but I am not sure could anyone that can read a log please tell me if there is anything else left in the computer. The computer now doesn't stay on-line it disconnects itself. I called the company that provides me with my internet service, and they said that I need a filter for the phone line. The person told me that, that will take care of the problem of the internet disconnecting. I think that it could be the virus I had in the computer. I wasn't able to get on-line for at least a week, I had gone and checked the disk for errors and finally the anti-virus program was able to find the virus's.