|I assume you've restarted the computer and its still the same.|
Although the symptoms don't fit too well you could try the EXE fix on the list here:
As you can't get online you will have to download the zip file on another computer. You will then have to extract the reg file on there too but whatever you do don't run it (if the other computer is not XP it could mess things up). Put the reg file on a flash drive and try double clicking it on the dud computer. As it is not a program (exe) it should run. OK all prompts, restart and see if it helps.
As there is a possibility it is malware (or the remnants of malware) you could download MalwareBytes freebie via another computer and a Flash Drive. Install it and run it.
If MalwareBytes won't run, change the download extension to either CMD or BAT. This also applies to MalwareBytes program file (mbam.exe). This feature was introduced to allow folk to use it even if their exe files have been blocked.
Always pop back and let us know the outcome - thanks