Hi Thorleaf and welcome to TSF !
If what adaware foiund were only tracking cookies then there's no reason to worry, everyone gets some while surfing the net and cleaning them monthly is sufficient. If it was something else than tracking cookies or MRU lists then report here.
Your rebooting problem is very likely to be hardware related. When a computer crashes wihtin a video intensive game it's usually because it fails to deliver enough power to the video card.
Post your system specs (see the link in my sig). If this is a desktop computer then open your case and tell us what you see on the sticker that's on the side of the power supply block : brand, model, total wattage and amperage on each rail.
Enter the BIOS at startup (usually by pressing the del key, else have a look at
this site) and search for a hardware monitor or pc health screen. Report what your cpu temp, fan speeds and +3.3, +5 and +12V voltages are.
Go to the event viewer : start => run => eventvwr.msc. Tell us whether you see any errors in one of the sections there that correspond to the times of the crashes.
Right-click my computer => properties => advanced => settings under startup and recovery => uncheck automatically restart. Tell us whether you see some blue screen now if the computer crashes again (please don't make it crash on purpose, you could end up with a corrupt system that wouldn't boot anymore).