Hi There,

I have several eMachines and Have experienced what you've described an as another said it was often the integral graphics engine at fault, put in a bargain  http://www.newegg.com/Product/Product.aspx?Item=N82E16814127368   or equivalent  

I like the eMachines, most of their issues are due not maintaining the firm ware updates from the manufacturers

Try BIOS Flash, download to CD, disconnect everything from the mobo except one RAM stick and the optical drive, slip the ISO image disc in and wait...........just let the machine fix itself..........could be 24 to 72 hrs burn-in time.

cheers!