Various Computer Issues

Basically my dad just gave me his old Sony Vaio since he's upgraded to new computer(s) and handed it down to me. When I turned it on and was messing with a few things I got an error message about Data Execution Process or something. It forces me to reboot, and when I relog I get this pop up:

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I did a quick virus scan using MalwareBytes and Symantec Antivirus, both turned up massive amounts of Adware, etc. I got all of that removed, I think, and was trying to install a few programs such as Maple, etc. When I got a pop up:

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Last thing that randomly started popping up after reboot was:

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I'm usually pretty good about fixing minor issues, but this whole thing just seems like a total cluster pineapple. I'm not sure if I should try and reformat, since I know this computer still has a lot of sensitive business related information of my dad's, and don't want to risk losing any of it. Any help would be greatly appreciated ;-;