please start by uninstalling any free software associated with PUPs and adware from the PC. You should search for each entry in the Remove list so you can decide which software to keep.
Please also check the browser’s shortcut (target field) on start menu or task bar because many malicious software now add their URL in front of the executable so the browser launches the malicious page automatically when it starts.
Then install a trial version of one of the leading antimalware solutions if you don’t have one installed already. That will prevent silent reinstalls of most PUP and adwares while you continue the cleaning.
You should also run msconfig.exe and check the services tab (hide all Microsoft services) and especially the startup tab. Investigate every entry and check if they are legit or not (don’t jump in to conclusions, take your time, you might remove legitimate components). Based on your startup tab analysis, check the registry entries referenced there and remove the ones associated with malware. This will prevent the system from loading and reinstalling malware automatically at startup.
If you haven’t done so, please also run combofix on the PC. It has saved me from some tough situations.
After each pass, check what is still there to remove and search the web on how to remove that, and go from there.
Once a PC becomes so filled with trash, it really becomes an uphill battle…