OtShot troubles, intermittent internet and system slowdown.

Hello and thank you in advance for any help you can offer! My PC had been running great until my Norton 360 subscription ran out and since I'm upgrading my system soon, I thought it best to just download a free AVAST until I do upgrade. Since then after an installation of Skype, OtShot downloaded itself along with Skype and although I removed it from my PC, it still attempts to initialize everytime I boot up. I've noticed an increasing ammount of issues with my PC, scoping from online gaming latency issues, difficulty installing updates or applications from discs, internet connection dropoffs, toggling from being connected to local only to no available connections then right back to normal connections. I realize this might be a hardware issue, but I've also very recently had trouble with my keyboard, specifically the "L", "O", ".", keys as well as my arrow keys and some numpad numbers. I wouldn't have even mentioned this issue, but I've replaced my keyboard twice since the issue began, each with a brand new one and it still persists, although only intermittently. Also, my system as a whole, whether browsing, gaming, or working (compiling data for my grad project) has been running very noticably slower. Please help!

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