there was a malware/spybot access on my computer. help??

So I was on my macbook pro and I didn't visit any questionable sites. The one thing I did last night though was searching online for sites to stream a tv show (which lead me to a bunch of shady sites that weren't sidereel or hulu).

Later on that night, I couldn't control my pointer with my tracker pad.

Basically, I sat there and kept on trying to do stuff but the cursor wouldn't obey me. So I stopped and just watched it. I saw my cursor move on its own, attempt to create a new folder on my desktop so I shut down my computer. Then I turned my computer back on (still connected to the same wifi) and the cursor just kept on "fighting me" for control. Eventually I just sat there and watched it. I saw the cursor go and attempt to open my resume folder (which of course held my email/phone number/address/etc) so I quickly shut down my computer.

I am back on it tonight and I don't seem to be having any problems. But that really freaked me out.

It seems that somebody definitely was able to access my computer and control it, which technically SHOULDN'T be possible since I have a brand new mac and I heard that it's suppose to come with software that has automatic anti-malware protection embedded in it.

Can somebody PLEASE explain to me what happened or what I should do. I'm rather concerned about this violation of privacy and I'm not sure if I should go get my entire system wiped just in case.

There may not be actual malware, but perhaps someone enabled the VNC server before you bought it (Was it new? Used? A store demo?) and is accessing it that way. However, it's hard to be sure from here. Rather than speculate, I would wipe the drive clean and reinstall OS X from scratch. You should make a complete system backup first, but DO NOT migrate your user data using the Migration Assistant. Manually restore any important documents, media, etc. I would also turn off your router until you have accomplished the reinstall.