Temporarily putting aside what Avira and Norton detected, IF you have both installed on your system, it might be contributing to your "drastic slowdown". If not the cause. Add to that, using more than one antivirus can cause system crashes, instability issues and false positives. One needs to be uninstalled.
With that said, I'm unable to read what Avira found, in your screenshot. It's too small. Kindly, post the information. Also include which operating system you're using. Are you experiencing any other problems, other than the slowdown?
An added note. System Restore was not designed as a virus/malware removal tool. System Restore backs up "the bad with the good". The success of its use, depends upon on the type of infection, and what was restored in the process.
I recently got a virus on my computer that is drastically slowing it down. I have already done a system restore twice hoping that would work, but nothing. I have also tried avira and norton, both have detected it but not removed. How can I go about cleaning this up? I have an image posted with a little info about what im dealing with. http://img17.imageshack.us/img17/3699/malwarev.jpg