Frankly have never seen a log like this one. The computer is obviously seriously infected. One reason being is you have no anti-virus program running at all.
Know you have tried Safe Mode, but have you tried downloading in Safe Mode with Networking?
Don't download and install just download to the desktop.
You are showing multiple instances of Spybot running, why?
Turn off Spybot TeaTimer it will interfere with any fixes.
I have to stress here HiJackThis is NOT a fixer program but a scanner program and using the Analyzer is just not recommended. If you have done fixes using that see if you can restore them.
Are you able to access ESET Online scanner or one of the other online scanners recommended in the Read Me Sticky at the top of the page?
Also please don't attach your logs, copy/paste them.