i need in depth instructions for a serious issue please

Im cleaning up a computer the neighbor gave me last year. My lap top took a nose dive and I decided to work the kinks out of the desk top. No matter what I do on the desk top, there are certain files that really do not mean anything from what I can figure or look up.... everytime I try to get rid of them there is a pop up box that states "This cannot be completed because the other user has cancelled the action" ...
Im getting really irked because that tells me someone has a hacked door into my system, N most likely its the neighbor that gave it to me in the first place, How do I find and wipe any malware that is allowing this travesty ??? I night be a computer nerd but this dude is a mechanical engineer, Im pretty sure he knows a few tricks to computers Ive never even heard of. I dont want to wipe everything because I have proof of his antics that would be lost and then I wouldnt have that stuff when I go to the police for his stalking.... long story, and this is just the latest in that line.
So in recap, I want to get rid of the malware that lets him remote control my computer without deleting everything that I will need later on for all the crap hes pulled.
Thanks
Lisa

 

If you are going to the police it is best to leave anything on it as is, they will want to see it all.

as for after, completely wipe the drive with a full format and preferably with Darik's Dban, boot and nuke.

you also want to contact any banks and change all passwords but not until pc is wiped as it is infected still.

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If I ever have stubborn files I generally turn them off using rkill, http://www.bleepingcomputer.com/download/rkill/

then delete using File Assassin from MWB https://www.malwarebytes.org/fileassassin/

Apart from regular MWB is also like Zone Alarm as an antivirus and Firewall. (M$ firewall is useless).

Plus This: http://www.bleepingcomputer.com/download/adwcleaner/
this: http://www.bleepingcomputer.com/download/combofix/ and this: http://www.bleepingcomputer.com/download/tdsskiller/

Finally, for routine maintence and driver file updates I use Slim Drivers and Slim Cleaner. https://www.slimwareutilities.com/index.php

And best of all, Free.

Not sure what the police are like in your part of the world, but here in the UK, unless you want a lot of hassle, you try to avoid them. Just saying.

 

1. Disconnect that computer from the Internet immediately.
2. Get someone experienced with computer hardware to check inside the case for any suspicious objects.
3. Use CloneZilla to take a backup of the whole drive before deleting anything, and send the backup to your neighbor.
4. From another computer, download the respective BIOS update tool for your motherboard, even if it's updated.
5. Burn the update files to a CD, and run the update.
6. Use DBAN to completely destroy all data inside the hard drive. (Might take 6 hours-4 days based on your drive size and CPU)
7. Install your preferred OS.
8. Get rid of "accessories" like keyboard, mouse, USB speaker, pendrive and such that your neighbor gifted to you.
9. Securely wipe all tools (USB sticks etc.) ever plugged into that computer and dispose the CD you used.
10. Don't let your neighbor spend time on your computer with an admin account. If he really has a malicious intent, he'll resort to tricks like "I'll do maintenance" or "I need to update something on it". Decline politely and tell him you've got <local tech store> updated it. (Perform step 3 so he doesn't have the "I need to get an important file I forgot on it" excuse)
11. Perform a virus check on all other computers on your network.