Random turn offs and memory usage

I received my MacBook Air as a gift from my aunt around December. She has had it before that for about a year. When I received it, all I use it for is for downloading and listening to music. I haven't downloaded anything else and I used the same user account as my aunt used (changed the name and picture and deleted her old documents). I should have plenty of space to download more stuff, but it is all being mysteriously used up! My music only accounts for 3.22 GB of storage, and the rest of my 62 GB are being used up by something else described as "Other."

I had a friend look at it for me, and he downloaded a software called GrandPerspective to see where all of my memory is being used up by. He found the files that were taking up all of the space and deleted them, giving me back nearly 50 GB. Those many files had strange names and weird file type extensions in their names. It was something to do with Yahoo email.

After looking through my Libraries files some more, he found folders called Virus Machine and VM. (He though VM meant Virus Machine.) He deleted "Virus Machine" and "VM" for fear that they were malicious to my laptop. One of the folders had a little red "no" sign on the bottom corner (I forget which one though). I had received a little more memory and it seemed that my problem was fixed.

After that, every time I use it, it ran EXTREMELY slow. Then it shut down right before my eyes and I cannot turn it on anymore. Please help!