So, the computer had been dreamy and slow, and a boot scan showed this trj.
Here are the fresh logs; even after all the procedures described in the other topics the boot scan still shows the same virus 
even after all the procedures described in the other topics the boot scan still shows the same virusof course, as no work have been done yet ;) a fix must be created first based on the logs you have attached
malware removers will be online later today
Have you been getting help elsewhere as there are a lot of logs on the system
CAUTION : This fix is only valid for this specific machine, using it on another may break your computer
Open notepad and copy/paste the text in the quotebox below into it:
CreateRestorePoint: HKLM\SOFTWARE\Policies\Microsoft\Internet Explorer: Policy restriction <======= ATTENTION Toolbar: HKLM - No Name - {CC1A175A-E45B-41ED-A30C-C9B1D7A0C02F} - No File Toolbar: HKU\S-1-5-21-1763470112-3753322355-1774201970-1000 -> No Name - {7FEBEFE3-6B19-4349-98D2-FFB09D4B49CA} - No File EmptyTemp: CMD: bitsadmin /reset /allusers
Save this as fixlist.txt, in the same location as FRST.exe
https://dl.dropboxusercontent.com/u/73555776/FRSTfix.JPG
Run FRST and press Fix
On completion a log will be generated please post that
THEN
Please download AdwCleaner by Xplode onto your desktop.
[*]Close all open programs and internet browsers.
[*]Double click on AdwCleaner.exe to run the tool.
[*]Click on Scan.
[*]After the scan is complete click on “Clean”
[*]Confirm each time with Ok.
[*]Your computer will be rebooted automatically. A text file will open after the restart.
[*]Please post the content of that logfile with your next answer.
[*]You can find the logfile at C:\AdwCleaner[S1].txt as well.
Help from somewhere else? No, I’m just plain stupid and made couple of runs before deciding to give up and ask for help.
Edit: Oh, and thanks for the help!
What location was avast reporting for bprotect ?
C:/Users/Mokidi/Local/Microsoft/Windows/Content.IE5/Temporary Internet Files/Y3F2WI59, if I’m not missing a folder
OK well the temp files have been emptied, how is the computer behaving ?
Better, though it still shows suspiciously high Physical memory usage (around 70-75%) and CPU usage - around 25%, while it isn’t running anything serious. Both should be lower. Yet it isn’t slow, which is a good sign.
I’ll run again a boot scan before going to bed to see what will it find and post the result in the morning.
The boot scan came clean. ;D
Thank you very much for the help, I apreciate it!
Subject to no further problems 
I will remove my tools now and give some recommendations, but, I would like you to run for 24 hours or so and come back if you have any problems
Now the best part of the day ----- Your log now appears clean 
A good workman always cleans up after himself so…The following will implement some cleanup procedures as well as reset System Restore points:
Remove tools
Download and run Delfix
https://dl.dropboxusercontent.com/u/73555776/delfix.JPG
Now that you are clean, to help protect your computer in the future I recommend that you get the following free programmes:
CryptoPrevent install this programme to lock down and prevent crypto ransome ware
https://dl.dropboxusercontent.com/u/73555776/CryptoPrevent.JPG
Update and run weekly to keep your system clean
Click on the link above to be taken to Unchecky.com
click the very large Download button.
click Save
Click Open folder
Right click on the Unchecky_setup and choose to Run as Administrator
Once open click the Install button.
Then click on Finish
Unchecky is now installed and will help you keep unwanted check boxes unchecked, this is a fire and forget programme 
It is critical to have both a firewall and anti virus to protect your system and to keep them updated.
To learn more about how to protect yourself while on the internet read this little guide Best security practices Keep safe 
Ok, thanks, downloaded and removed the cleaning software; the protection is running.
And I’ll be back to report tomorrow
Have a nice evening.
Update from today: Everything still looks clean.
Hopefully, I won’t need help removing anything else soon so - have a nice holiday and Happy Valentine!
Thank you