I would also like to mention here that you have said that you installed Trendmicro and then removed it...how did you remove it? Did you actually UNINSTALL it or just delete? Make sure it was uninstalled. One should never have more than one antivirus program running on the computer.
Then you said you installed avira antivirus and it DID find 34 infections. So it IS working. Keep it. It is an excellent FREE program, no need to install another.
Follow caperjack's instructions. You can also download Malwarebytes' Anti-Malware directly from their website also.
Be sure to reboot the computer AFTER running MBA-M and removing everything found.
Also download and run HiJackThis and post that log here once you have finished all other instructions