A simple delete on any file is permanent from the point of veiw that the file will not reappear or cause any more bother , but it can be retrieved by recovery software ,providing the file location has not been overwritten . however you are talking about something more sinister , viruses and spyware/malware, can often place nasties on your PC and create a duplicate elsware on the PC ,then a third file ,usually some form of command or scrypt, can cause the file to reappear after every reboot even though you beleive you deleted it .in this case you need to know the likely locations for the backup files .
often, after a scare ,I will check a few locations that are favorites for such problems ,for example C:>users/"username"/Appdata/local/Temp....
often are home to the files. Appdata is a hidden folder so you need to enable hidden files via ,folder and search options to progress past that . the contents of the temp folder can be deleted without problems ,though you cannot delete files that are running .
also worth checking msconfig to see if any startup programs have been created to trigger such nasties .
but you should not be needing to do any of that ,there are lots of options as far as antivirus programs go ,microsofts own security essentials is as good as any of them and is free.
it should be policy to allways scan any thing you download before opening .